Litton's Problematical Recreations What letter follows OTTFFSSE_?

(MEGALING INCOMPLETE)
N
Chapter 1: For the Perceptive
Problems of a general nature whose solutions The numbers are divided into three groups as follows:
require insight as the principal ingredient 0, 3, 6, 8, 9, … in the first group, 1, 4, 7, 11, 14, … in the
second group and 2, 5, 10, 12, 13, … in the third. In
.Rufus T. Flypaper drives two miles to work every which groups would 15, 16 and 17 be placed?
morning- Very precise, he knows he must average 30
mph to arrive on time. One morning a woman driver 15 and 16 in the third group, 17 in the second
impedes him for the first mile, cutting his average to only group
l5 mph. He quickly calculated his proper speed for the
rest of his trip to arrive on time. Assume that his car In a fast Major League baseball game, pitcher Hi N.
could do 120 mph. Could he arrive on time? Outside managed to get by with the minimum number
of pitches possible. He played the entire game, which
No; he has already used 4 minutes, the time that was not called prior completion. How many pitches did
he has to go the whole 2 miles. he make?

Stations A and B are 120 miles apart on a single-track 25

railroad. At the same time that a train leaves A for B at
25 mph, a train leaves B for A at 15 mph. Just as the Determine the next three terms of the sequence 12, 1,
first train leaves A, a South American botfly flies from 1, 1, …
the front of the engine straight toward the other train at
100 mph. On meeting the second train it immediately 2, 1, and 3
turns back and flies straight for the first train. It continues
to fly back and forth with undiminished speed until it is [MAY 2017] What is the least number of links that must
crushed in the eventual collision. How far had the fly be disengaged from a 23-link chain so that any number
flown? of links from 1 to 23 can be obtained by taking one or
more of the pieces?
300 miles
Two (4th and 11th chain)
Maynard's Grandfather Clock is driven by two weights,
one for the striking mechanism which strikes the hours The set A contains the integers 0, 4, 5, 9, 11, 12, 13, 14,
only, the other for the time mechanism. When he hears 19, … The set B contains 1, 2, 3, 6, 7, 8, 10, 15, 16, 17,
the clock strike his bedtime, he immediately winds the 18, … Place the 20 and 21 in their proper sets.
clock and retires. After winding, the weights are exactly
opposite each other. The weights are again opposite 20 is in A, 21 is in B
every six hours thereafter. What is Maynard's bedtime?
How many colors are necessary for the squares of a
9 p.m. or 3 a.m. chessboard in order to assure that a bishop cannot
move from one square to another of the same color?
Two squares are removed from opposite corners of a
checkerboard leaving 62 squares. Can the 8 colors
checkerboard be filled with 31 dominoes, each domino
covering two adjacent squares? A neat computer programmer wears a clean shirt every
day. If he drops off his laundry and picks up the previous
No week’s load every Monday night, how many shirts must
he own to keep him going?
[MAY 2017] Assuming the sun rises at 6:00 a.m., sets
at 6:00 p.m., and moves at a uniform rate, how can a 15 shirts
lost boy scout determine south by means of a watch on
a cloudless day? [MAY 2019] The passengers on an excursion bus
consisted of 14 married couples, 8 of whom brought no
Align the hour hand with the sun’s azimuth, and children, and 6 of whom brought 3 children apiece.
south will be midway between the hour hand and Counting the driver, the bus had 31 occupants. How is
12. this possible?

Included among the 18 children were 8 married

couples
Very few people are aware of the growth pattern of Chapter 2: For Sleuths
Jack’s beanstalk. On the first day it increased its height Problems requiring careful analysis and logical
by 1/2, on the second day by 1/3, on the third day by deduction
1/4, and so on. How long did it take to achieve its
maximum height (100 times its original height)? On a certain campus liberal arts students always lie and
engineers always tell the truth. A stranger meets 3
198 days students and asks the first if he is studying liberal arts.
The first answers the question, but the stranger doesn't
A jig-saw puzzle contains 100 pieces. A "move" consists hear him. The second student then says that the first
of connecting two clusters (including "clusters" of just denied being a liberal arts student. Then the third
one piece.) What is the minimum number of moves student says that the first is really a liberal arts student.
required to complete the puzzle. How many are Iiberal arts students? Can we decide
which?
99 moves
1, the first
[NOV 2023] A novice librarian shelved a twelve-volume
set of encyclopedias in the following order from left to Four boys, Alan, Brian, Charles, and Donald, and four
right. Volume 8, 11, 5, 4, 9, 1, 7, 6, 10, 3, 12, and 2. girls, Eve, Fay, Gwen, and Helen are each in love with
Using her system, where will the annual supplement, one of the others, and, sad to say, in no case is their
Volume 13, go? love requited. Alan loves the girl who loves the man who
loves Eve. Fay is loved by the man who is loved by the
Between volumes 10 and 3 girl loved by Brian. Charles loves the girl who loves
Donald. If Brian is not loved by Gwen, and the boy who
With some sharp reasoning, you ought to be able to is loved by Helen does not love Gwen, who loves Alan?
determine the last member of the sequence for which
the first 20 members are: 11, 31, 71, 91, 32, 92, 13, 73, Gwen loves Alan
14, 34, 74, 35, 95, 16, 76, 17, 37, 97, 38, 98, ?
A canoe is floating in a swimming pool. Which will raise
79 the level of the water in the pool higher, dropping a
penny into the pool or into the canoe? Or does it make
[NOV 2021] A lighthouse shows successive one-second any difference?
flashes of red, white, green, green, white, red. A second
lighthouse does the same only with two-second flashes. Dropping it into the canoe will raise the water level
The six-second sequence of the first lighthouse is higher.
repeated steadily, as is the twelve-second sequence of
the other lighthouse. What fraction of the time do the Five suspects were rounded up in connection with the
two lights show the same color if the given sequences famous "Cock Robin Murder.” Their statements were as
start at the same time? follows: A: "C and D are lying.” B: "A and E are lying.” C:
"B and D are lying.” D: "C and E are lying.” E: "A and B
1/6 are lying.” Who is lying?

Four players played a hand of hearts at $1 a point A is lying

(pairwise payoffs). Dave lost $10 to Arch, $12 to Bob,
and $20 to Chuck. How many hearts did poor Dave Six grocers in a town each sell a different brand of tea
take in? in four-ounce packets at 25 cents per packet. One of the
grocers gives short weight, each packet of his brand
4 hearts and the queen of spades weighing only 3 3/4 ounces. If I can use a balance for
only one weighing, what is the minimum amount I must
spend to be sure of finding the grocer who gives short
weight?

3.7 dollars
Between Kroflite and Beeline are five other towns. The Chapter 3: For Gamblers
seven towns are an integral number of miles from each Problems involving probability and determination
other along a straight road. The towns are so spaced of the number of outcomes of various situations
that if one knows the number of miles a person has
traveled between any two towns, he can determine the A gambler devised a game to be played with a friend.
particular towns uniquely. What is the minimum distance He bet 1/2 the money in his pocket on the toss of a coin;
between Kroflite and Beeline to make this possible? heads he won, tails he lost. The coin was tossed, and
the money handed over. The offer was repeated, and
25 miles the game continued. Each time the bet was for 1/2 the
money then in his possession. Eventually the number of
In the game "subtract-a-square," a positive integer is times he lost was equal to the number of times he won.
written down and two players alternately subtract Quickly now! Did he gain, lose, or break even?
squares from it with the restriction that the remainder
must never be Iess than zero. The player who leaves He lost
zero wins. What square should the first player subtract
if the original number is 29? A prisoner is given 10 white balls, 10 black balls and two
boxes. He is told that an executioner will draw one ball
9 from one of the two boxes. If it is white, the prisoner will
go free; if it is black, he will die. How should the prisoner
A lamp has three on-off buttons, all of which must be on arrange the balls in boxes to give himself the best
for the lamp to light. A man wishes to turn on the lamp chance for survival?
at a moment when only the second switch is off. He
does not know this and proceeds to press the first 1 white ball in one box and the remaining balls in
button. Getting no result, he presses the second and the other box (73.7%)
eventually, on the seventh trial, (never repeating any on-
off configuration), the lamp finally lights. In what order [NOV 2019] Smith and Jones, both 50% marksmen,
did he press the buttons? decide to fight a duel in which they exchange alternate
shots until one is hit. What are the odds in favor of the
1-2-3-2-1-2-3 man who shoots first?

A game proceeds as follows: Smith starts with a 10-link 2/3

chain and removes any single link, presenting Jones
either with a 9-link chain or two chains having a total of There are n points on a circle. A straight-line segment is
9 links. Jones removes any one link from each of the drawn between each pair of points. How many
chains. Smith removes any one link from each of the intersections are there within the circle if no 3 lines are
remaining chains and so on, until the winner removes collinear?
the last link or links. What should Smith do first?
nC4 or nP4 / 24
Leave two chains of 6 and 3 links
On a certain day, our parking lot contains 999 cars, no
[APR 2023] In Bristol 90% of the citizens drink tea; 80% two of which have the same 3-digit license number. After
drink coffee; 70% drink whiskey; and 60% drink gin. No 5:00 p.m. what is the probability that the license
one drinks all four beverages. What percent of Bristol’s numbers of the first 4 cars to leave the parking lot are in
citizen drink liquor? increasing order of magnitude?

100% drink liquor 1/24

[MAY 2017] You and a friend spot a loose $20 bill [NOV 2016] Three marksmen simultaneously shoot at
simultaneously and agree to an auction in which you and hit a rapidly spinning spherical target. What is the
write down your bids and compare them. High bidder probability that the three points of impact are on the
gets the $20 and pays the other the amount of the same.
higher bid. Tie bidders split the $20. How much do you
bid? 1

$9.99
A hospital nursery contains only two baby boys; the girls Three dart players threw simultaneously at a tic-tac-toe
have not yet been counted. At 2:00 p.m. a new baby is board, each hitting a different square. What is the
added to the nursery. A baby is then selected at random probability that the three hits constituted in a win at tic-
to be the first to have its footprint taken. It turns out to tac-toe?
be a boy. What is the probability that the Iast addition to
the nursery was a girl? 2/21

2/5 Four swimming pool builders submit sealed bids to a

homeowner who is required by law to accept the last bid
Assume that a single depth charge has a probability of that he sees, i.e., once he looks at a bid, he
1/2 of sinking a submarine, 1/4 of damage and 1/4 of automatically rejects all previous bids. He is not
missing. Assume also that two damaging explosions required to open all the envelopes, of course. Assuming
sink the sub. What is the probability that 4 depth that all four bids are different, what procedure will
charges will sink the sub? maximize his chances of accepting the lowest bid. and
what will be the probability of doing so?
251/256
11/24
What is the most likely distribution of the suits in a
hand at Bridge? All the members of a fraternity play basketball while all
but one play ice hockey; yet the number of possible
4-4-3-2 basketball teams (5 members) is the same as the
number of possible ice hockey teams (6 members).
If 2 marbles are removed at random from a bag Assuming there are enough members to form either
containing black and white marbles, the chance that type of team, how many are in the fraternity?
they are both white is 1/3. If 3 are removed at random,
the chance that they all are white is 1/6. How many 15
marbles are there of each color?
A game of super-dominoes is played with pieces divided
w = 6; b = 4 into three cells instead of the usual two, containing all
combinations from triple blank to triple six, with no
An expert gives team A only a 40% chance to win the duplications. For example, the set does not include both
World Series. Basing his calculation on this a gambler 1 2 3 and 3 2 1 since these are merely reversals of each
offers 6 to 5 odds on team B to win the first game. Is his other. (But it does contain 1. 3 2.) How many pieces are
judgment sound? there in a set?

Yes 196 pieces

A salesman visits ten cities arranged in the form of a Martian coins are 3-sided (heads, tails, and torsos),
circle, spending a day in each. He proceeds clockwise each side coming up with equal probability. Three
from one city to the next, except whenever leaving the Martians decided to go odd-man-out to determine who
tenth city he may go to either the first or jump to the pays a dinner check. (If two coins come up the same
second city- How many days must elapse before his and one different, the owner of the latter coin foots the
location is completely indeterminate, i.e., when he could bill). What is the expected number of throws needed in
be in any one of the ten cities? order to determine a loser?

83 days 1.5 throws

A coin is so unbalanced that you are likely to get two There are three families, each with two sons and two
heads in two successive throws as you are to get tails daughters. In how many ways can all these young
in one. What is the probability of getting heads in a people be married?
single throw?
80 ways
0.618
How many three-digit telephone area codes are In a carnival game, 12 white balls and 3 black balls are
possible given that: (a) the first digit must not be zero or put in an opaque bottle, shaken up, and drawn out one
one; (b) the second digit must be zero or one; (c) the at a time. The player gets 25 cents for each white ball
third digit must not be zero; (d) the third digit may be one which emerges before the first black ball. If he pays one
only if the second digit is zero. dollar to play, how much can he expect to win (or lose)
on each game.
136 possible codes
Average loss of a quarter a game
Six men decide to play Russian roulette with a six-gun
loaded with one cartridge. They draw for position, and In the binary system there are only two positive integers
afterwards' the sixth man casually suggests that containing no digit more than once, namely 1 and 10.
instead of letting the chamber rotate in sequence, each How many are there in base ten?
man spin the chamber before shooting. How would this
improve his chances? 8,677,690 integers

0.1 In the final seconds of the game, your favorite N.B.A.

team is behind 117 to 118. Your center attempts a shot
A long shot poker player draws two cards to the five and and is fouled for the 2nd time in the last 2 minutes as
six of diamonds and the joker. What are his chances of the buzzer sounds. Three to make two in the penalty
coming up with a pat hand? (straight or flush) situation. Optimistic? Note: the center is only a 50% free
thrower. What are your team's overall chances of
0.168 winning?

In Puevigi, the game of craps is played with a referee 11/16 (69%)

calling the point by adding together the six faces (three
on each die) visible from his vantage point. What is the One of a pair of dice is loaded so that the chance of a 1
probability of making 16 the hard way? (That is, by turning up is 1/5, the other faces being equally likely. Its
throwing two eights.) mate is loaded so that the chance of a 6 turning up is
1/5, the other faces being equally likely. How much does
0 this loading increase the probability of throwing a 7 with
the two dice?
Max and his wife Min each toss a pair of dice to
determine where they will spend their vacation. If either 1/750
of Min's dice displays the same number of spots as
either of Max's, she wins, and they go to Bermuda. If all the 720 permutations of the digits 1 through 6 are
Otherwise, they go to Yellowstone. What is the chance arrange in numerical order, what is the 417th term?
they'll see "Old Faithful" this year?
432516
0.486
The local weather forecaster says, “no rain” and his
There are four volumes of an encyclopedia on a shelf, record is 2/3 accuracy of prediction. But the Federal
each volume containing 300 pages, (that is, numbered Meteorological Service predicts rain, and their record is
1 to 600), but these have been placed on the shelf in 3/4. With no other data available, what is the chance of
random order. A bookworm starts at the first page of Vol. rain?
1 and eats his way through to the last page of Vol. 4.
What is the expected number of pages (excluding 3/5
covers) he has eaten through?
A sharp operator makes the following deal. A player is
500 pages to toss a coin and receive 1, 4, 9, … n^2 dollars if the
first head comes up on the first, second, third, … n-th
Venusian batfish come in three sexes, which are toss. The sucker pays ten dollars for this. How much can
indistinguishable (except by Venusian batfish). How the operator expect to make if this is repeated a great
many live specimens must our astronauts bring home in many times?
order for the odds to favor the presence of a “mated
triple” with its promise of more little batfish to come? 6

Five specimens (50/81)

In 1969, the World Series began in the stadium of Chapter 4: For the Algebraically Inclined
American League pennant winner. Assume the Problems best attacked by means of variables and
contenders are evenly matched. What is the probability equations
that the series ended where it began?
To stimulate his son in the pursuit of partial differential
5/8 equations, a math professor offered to pay him $8 for
every equation correctly solved and to fine him $5 for
In a carnival game 5 balls are tossed into a square box every incorrect solution. At the end of 26 problems,
divided into 4 square cells, with baffles to insure that neither owed any money to the other. How many did the
every ball has an equal chance of going in any cell. The boy solve correctly?
player pays $1 and receives $1 for every cell which is
empty after the 5 balls are thrown. How much does the 10 problems
operator expect to make per game?
An expert on transformer design relaxed one Saturday
5¢ by going to the races. At the end of the first race, he had
doubled his money. He bet $30 on the second race and
Having lost a checker game, a specialist in learning tripled his money. He bet $54 on the third race and
programs threw one of the red checkers out the window. quadrupled his money. He bet $72 on the fourth race
His wife reboxed the 12 black pieces and 11 red pieces and lost it, but still had $48 left. With how much money
one at a time in random fashion. The number of black did he start?
checkers in the box always exceeded the number of
reds. What was the a priori probability of this 29$
occurrence.
Between Sing-Sing and Tarry-Town,
1/23 I met my worthy friend, John Brown,
And seven daughters, riding nags,
And everyone had seven bags.
In every bag were thirty cats,
And every cat had forty rats,
Besides a brood of fifty kittens.
All but the nags were wearing mittens!
Mittens, kittens - cats, rats - bag, nags - Browns,
How many were met between the towns?

764,488

Dr. Reed, arriving late at the lab one morning, pulled out
his watch and said, "I must have it seen to. I have
noticed that the minute and the hour hand are exactly
together every sixty-five minutes.” Does Dr. Reed's
watch gain or lose, and how much per hour?

60/143 minutes

At this moment, the hands of a clock in the course of

normal operation describe a time somewhere between
4:00 and 5:00on a standard clock face. Within one hour
or less, the hands will have exactly exchanged
positions; what time is it now?

4:26.85
Two men are walking towards each other at the side of A necklace consists of pearls which increase uniformly
a railway. A freight train overtakes one of them in 20 from a weight of 1 carat for the end pearls to a weight of
seconds and exactly ten minutes later meets the other 100 carats for the middle pearl. If the necklace weighs
man coming in the opposite direction. The train passes altogether 1650 carats and the clasps and string
this man in l8 seconds. How long after the train has together weigh as much (in carats) as the total number
passed the second man will the two men meet? of pearls, how many pearl does the necklace contain?
(Constant speeds are to be assumed throughout.)
33 pearls
5562 seconds
A pupil wrote on the blackboard a series of fractions
[NOV 2023] Using the French Tricolor as a model, how having positive integral terms and connected by signs
many flags are possible with five available colors if two which were either all * or all X, although they were so
adjacent rows must not be colored the same? carelessly written it was impossible to tell which they
were. It still wasn't clear even though he announced the
50 flags result of the operation at every step. The third fraction
had denominator 19. What was the numerator?
A cubic box with sides ‘a’ feet long is placed flat against
a wall. A ladder ‘p’ feet long is placed in such a way that 25
it touches the wall as well as the free horizontal edge of
the box. If a = 1 and p = sqrt(15), calculate at what height Jai Alai balls come in boxes of 8 and 15; so that 38 balls
the ladder touches the wall from the floor. (one small box and two large) can be bought without
having to break open a box, but not 39. What is the
3.63 or 1.38 feet maximum number of balls which cannot be bought
without breaking boxes?
[NOV 2017] Dr. Irving Weiman, who is always in a hurry,
walks up an up-going escalator at the rate of one step 97 balls
per second. Twenty steps bring him to the top. Next day
he goes up at two steps per second, reaching the top in A parking lot charges X for the first hour or fraction of an
32 steps. How many steps are there in the escalator? hour and 2/3 of X for each hour or fraction thereafter.
Smith parks 7 times as long as Jones but pays only 3
80 steps times as much. How long did each park? (The clock
registers only 5-minute intervals.)
Citizens of Franistan pay as much income tax
(percentagewise) as they make rupees per week. What Jones parked for 0.5 hour and Smith for 3.5 hours.
is the optimal salary in Franistan?
Mr. Field, a speeder, travels on a busy highway having
50 rupees the same rate of traffic flow in each direction. Except for
Mr. Field, the traffic is moving at the legal speed limit.
There are nine cities which are served by two competing Mr. Field passes one car for every nine which he meets
airlines. One or the other airline (but not both) has a from the opposite direction. By what percentage is he
flight between every pair of cities. What is the minimum exceeding the speed limit?
number of triangular flights (i.e., trips from A to B to C
and back to A on the same airline)? 25%

12 triangular flights What is the millionth term of the sequence 1, 2, 2, 3, 3,

3, 4, 4, 4, 4, … in which each positive integer n occurs
in blocks of n terms?
Two snails start from the same point in opposite
directions toward two bits of food. Each reaches his 1,414
destination in one hour. If each snail had gone in the
direction the other took, the first snail would have The teacher marked the quiz on the following basis: one
reached his food 35 minutes after the second. How do point for each correct answer, one point off for each
their speeds compare? question left blank and two points off for each question
answered incorrectly. Pat made four times as many
The first snail traveled at three-fourths the speed errors as Mike, but Mike left nine more questions blank.
of the second. If they both got the same score, how many errors did
each make?

Pat made eight errors and Mike made two errors

A student, just beginning the study of logarithms, was Chapter 5: For the Geometrically Inclined
required to evaluate an expression of the form of (log Problems involving plane geometry and
A)/(log B). He proceeded to cancel common factors in trigonometry
both numerator and denominator, (including the “factor”
log), and arrived at the result 2/3. Surprisingly, this was A forgetful physicist forgot his watch one day and asked
correct. What were the values of A and B? an E.E. on the staff what time it was. The E.E. Iooked at
his watch and said: “The hour, minute, and sweep
A = 9/4, B = 27/8 second hands are as close to trisecting the face as they
ever come. This happens only twice in every 12 hours,
[MAY 2017] There are four towns at the corners of a but since you probably haven't forgotten whether you
square. Four motorists set out, each driving to the next ate lunch, you should be able to calculate the time.”
(clockwise) town, and each man but the fourth going 8 What time was it to the nearest second?
mph faster than the car ahead – thus the first car travels
24 mph faster than the fourth. At the end of one hour the 2:54:35 or 9:5:25
first and third cars are 204, and the second and fourth
212 (beeline) miles apart. How fast is the first car The faces of a solid figure are all triangles. The figure
traveling and how far apart are the towns? has nine vertices. At each of six of these vertices, four
faces meet, and at each of the other three vertices, six
50 mph, 180 miles faces meet. How many faces does the figure have?

Solve the equation sqrt(x + sqrt(x + sqrt(x + … = sqrt(x 14 faces

sqrt(x sqrt x … where both members represent infinite
expressions. [NOV 2017] A new kind of atom smasher is to be
composed of two tangents and a circular arc which is
x = 0 or 2 concave towards the point of intersection of the two
tangents. Each tangent and the arc of the circle is 1 mile
[APR 2023] A pencil, eraser and notebook together cost long. What is the radius of the circle?
$1.00. A notebook costs more than two pencils, and
three pencils cost more than four erasers. If three 1437.45 feet
erasers cost more than a notebook, how much does
each cost? A spider and a fly are located at opposite vertices of a
room of dimensions 1, 2 and 3 units. Assuming that the
P = $26, E = $19, N = $55 fly is too terrified to move, find the minimum distance
the spider must crawl to reach the fly.

Sqrt(18) units

[NOV 2017] In a room 40 feet long, 20 feet wide, and

20 feet high, a bug sits on an end wall at a point one foot
from the floor, midway between the sidewalls. He
decides to go on a journey to a point on the other end
wall which is one foot from the ceiling midway between
the sidewalls. Having no wings, the bug must make this
trip by sticking to the surfaces of the room. What is the
shortest route that the bug can take?

58 feet

A circle of radius I inch is inscribed in an equilateral

triangle. A smaller circle is inscribed at each vertex,
tangent to the circle and two sides of the triangle. The
process is continued with progressively smaller circles.
what is the sum of the circumference of all circles.

5π
[NOV 2023] A farmer owned a square field measuring A one-acre field in the shape of a right triangle has a
exactly 2261 yards on each side. 1898 yards from one post at the midpoint of each side. A sheep is tethered to
corner and 1009 yards from an adjacent corner stood a each of the side posts and a goat to the post on the
beech tree. A neighbor offered to purchase a triangular hypotenuse. The ropes are just long enough to let each
portion of the field stipulating that a fence should be animal reach the two adjacent vertices. What is the total
erected in a straight line from one side of the field to an area the two sheep have to themselves, i.e., the area
adjacent side so that the beech tree was part of the the goat cannot reach?
fence. The farmer accepted the offer but made sure that
the triangular portion was of minimum area. What was 1 acre
the area of the field the neighbor received, and how long
was the fence? A divided highway goes under a number of bridges, the
arch over each lane being in the form of a semi-ellipse
939,120 square yards, 2018 yards with the height equal to the width. A truck is 6 ft. wide
and 12 ft. high. What is the lowest bridge under which it
A man leaves from the point where the prime meridian can pass?
crosses the equator and moves forty-five degrees
northeast by geographic compass which always points 13 ft. 5 in. high
toward the north geographic pole. He constantly
corrects his route. Assuming that he walks with equal A cowboy is five miles south of a stream which flows due
facility on land and sea, where does he end up and how east. He is also 8 miles west and 6 miles north of his
far will he have travelled when he gets there? cabin. He wishes to water his horse at the stream and
return home. What is the shortest distance he can travel
10^7 sqrt(2) meter and accomplish this?

Near the town of Lunch, Nebraska there is a large 17.9 miles

triangular plot of land bounded by three straight roads
which are 855, 870, and 975 yards long respectively. While still at a sizable distance from the Pentagon
The owner of the land, a friend of mine, told me that he building, a man first catches sight of it. Is he more likely
had decided to sell half the plot to a neighbor, but that to be able to see two sides or three?
the buyer had stipulated that the seller of the land
should erect the fence which was to be a straight one. Equal probability of 1/2
The cost of fences being high, my friend naturally
wanted the fence to be as short as possible. What is the A pirate buried his treasure on an island, a conspicuous
minimum length the fence can be? landmark of which were three palm trees, each one 100
feet from the other two. Two of these trees were in a N-
600 yards S line. The directions for finding the treasure read:
“Proceed from southernmost tree 15 feet due north,
Three hares are standing in a triangular field which is then 26 feet due west.” Is the treasure buried within the
exactly 100 yards on each side. One hare stands at triangle formed by the trees?
each corner; and simultaneously all three set off
running. Each hare runs after the hare in the adjacent The treasure lies outside
corner on his left, thus following a curved course which
terminates in the middle of the field, all three hares An Origami expert started making a Nani-des-ka by
arriving there together. The hares obviously ran at the folding the top left corner of a sheet of paper until it
same speed, but just how far did they run? touched the right edge and the crease passed through
the bottom left corner. He then did the same with the
100 yards lower right corner, thus making two slanting parallel
lines. The paper was 25 inches long and the distance
Scalene triangle ABC, which is not a right triangle, has between the parallel lines was exactly 7/40 of the width.
sides which are integers. If sin A = 5/13, find the smallest How wide was the sheet of paper?
values for its sides, i.e., those values which make the
perimeter a minimum. 24 in

a = 25, b = 16, c = 39 The Ben Azouli are camped at an oasis 45 miles west
of Taqaba. They decide to dynamite the Trans-
Hadramaut railroad joining Taqaba to Maqaba, 60 miles
north of the oasis. If the Azouli can cover 18 miles a day,
how long will it take them to reach the railroad?

Two days
[NOV 2017] A cross section through the center of a Chapter 5: For Fans of Diophantus
football is a circle x inches in circumference. The football Problems involving Diophantine equations, those
is x – 8 inches long from the tip to tip and each seam is for which only whole number solutions are sought
an arc of a circle ¾ if x inches in diameter. Find x.
Find the smallest number (x) of persons a boat may
20.69 in carry so that (n) married couples may cross a river in
such a way that no woman ever remains in the company
A yang, ying, and yung is constructed by dividing a of any man unless her husband is present. Also find the
diameter of a circle, AB, into three parts by points C and least number of passages (y) needed from one bank to
D, then describing on one side of AB semicircles having the other. Assume that the boat can be rowed by one
AC and AD as diameters and on the other side of AB person only.
semicircles having BD and BC as diameters. Which is
larger, the central portion or one of the outside pieces? n = 2, x = 2, y = 5

All three are the same size A, B, and C participate in a track meet, consisting of at
least three events. A certain number of points are given
A diaper is in the shape of a triangle with sides 24, 20 for first place, a smaller number for second place, and a
and 20 inches. The long side is wrapped around the still smaller number for third place. A won the meet with
baby’s waist and overlapped two inches. The third point a total score of 14 points; B and C are tied for second
is brought up to the center of the overlap and pinned in with 7 points apiece. B won first place in the high jump.
place. The pin is to go through three thicknesses of Who won the pole vault assuming no ties occurred in
material. What is the area in which the pin may be any event?
placed?
A won the pole vault
2.5 square in
Find the simplest solution in integers for the equation
[NOV 2016] A coffee pot with a circular bottom tapers (1/x^(2)) + (1/y^(2)) = (1/z^(2)).
uniformly to a circular top with radius half that of the
base. A mark halfway up the side says “2 cups.” Where x = 15, y = 20, z = 12
should the “3 cups” mark go? What is the capacity of the
pot? Maynard the Census Taker visited a house and was
told, “Three people live there, The product of their ages
2% of the way down from the top, 3 1/37 cups is 1296, and the sum of their ages is our house number.”
After an hour of cogitation Maynard returned for more
[MAY 2018] An icicle forming from a dripping gutter is in information. The house owner said, “I forgot to tell you
the shape of a cone five times as long as it is wide (at that my son and grandson live here with me.” How old
the top). A few hours later it has doubled in length and were the occupants and what was their street number?
the generating angle has also doubled. How does its
present weight compare with its previous weight? Ages: 1, 18, and 72
Street number: 91
Almost 33 times
In Byzantine basketball there are 35 scores which are
There is one flag at the entrance to a racetrack and impossible for a team to total, one of them being 58.
another inside the track, half a mile from the first. A Naturally a free throw is worth fewer points than a field
jockey notes that no matter where he is on the track, goal. What is the point value of each?
one flag is 3 times as far away as the other. How long is
the track? Free throw: 8
Field goal: 11
1980π
Gherkin Gesundheit, a brilliant graduate mathematics
What is the longest 6' wide shuffleboard court which will student, was working on an assignment but, being a bit
fit in a 20’ x 30’ rectangular room? absent-minded, he forgot whether he was to add or to
multiply the three different integers on his paper" He
30.875 decided to do it both ways and, much to his surprise, the
answer was the same. What were the three different
integers?

1, 2, 3
[NOV 2022] Three farmers, Adams, Brown and Clark all In European countries the decimal point is often written
have farms containing the same number of acres. a little above the line. An American, seeing a number
Adams' farm is most nearly square, the length being written this way, with one digit on each side of the
only 8 miles longer than the width. Clark has the most decimal point, assumed the numbers were to be
oblong farm, the length being 34 miles longer than the multiplied. He obtained a two-digit number as a result
width. Brown's farm is intermediate between these two, but was 14.6 off. What was the original number?
the length being 28 miles longer than the width. If all the
dimensions are in exact miles, what is the size of each 5.4
farm?
Two wheels in the same plane are mounted on shafts
40x48, 32x60, 30x64 13 in. apart. A belt goes around both wheels to transmit
power from one to the other. The radii of the two wheels
1960 and 1961 were bad years for ice cream sales but and the length of the belt not in contact with the wheels
1962 was very good. An accountant was looking at the at any moment are all integers - How much larger is one
tonnage sold in each year and noticed that the digital wheel than the other?
sum of the tonnage sold in 1962 was three times as
much as the digital sum of the tonnage sold in 1961. 5 in
Moreover, if the amount sold in 1960 (346 tons), was
added to the 1961 tonnage, this total was less than the Five points are located in or on the perimeter of an
total tonnage sold in 1962 by the digital sum of the equilateral triangle with 9-inch sides. If d is the distance
tonnage sold in that same year. Just how many more between the closest pair of points, what is the maximum
tons of ice cream were sold in 1962 than in the previous possible value of d?
year?
4.5 in
361 tons
If THAT = (AH)(HA), what is THAT?
Three rectangles of integer sides have identical areas.
The first rectangle is 278 feet longer than wide. The 6786
second rectangle is 96 feet longer than wide. The third
rectangle is 542 feet longer than wide. Find the area and A group of hippies are pondering whether to move to
dimensions of the rectangles. Patria, where polygamy is practiced but polyandry and
spinsterhood are prohibited, or Matria, where polyandry
Area: 1,466,640 ft2 is permitted, and polygamy and bachelorhood are
Dimensions: 1080x1358, 1164x1260, 970x1512 proscribed. In either event the possible number of
“arrangements” is the same. The girls outnumber the
When little Willie had sold all his lemonade, he found he boys. How many are there?
had $7.95 in nickels, dimes, and quarters. There were
47 coins altogether and, having just started to study 4 girls and 2 boys
geometry, he noticed that the numbers of coins satisfied
a triangle inequality, i.e., the sum of any two Dad and his son have the same birthday. On the last
denominations was greater than the third. How many of one, Dad was twice as old as Junior. Uncle observed
each were there? that this was the ninth occasion on which Dad's birthday
age had been an integer multiple of Junior's. How old is
D = 20, Q = 32, N = 4 Junior?

There are 100 coins in a piggy bank totaling $5.00 in Junior: 36

value, the coins consisting of pennies, dimes, and half Dad: 72
dollars. How many of each are there?

P = 60, D = 39, H = 1

Every year engineering consultant pays a bonus of

$300 to his most industrious assistant, and $75 each to
the rest of his staff. After how many years would his outlay
be exactly $6,000 if all but two of his staff had merited the
$300 bonus, but none of them more than twice?

Years: 8
Staff: 7
 Chapter 7: For Number Theorists My house is on a road where the numbers run 1, 2, 3,
Problems involving properties of integers 4., - consecutively. My number is a three digit one and,
by a curious coincidence, the sum of all house numbers
The undergraduates of a School. of Engineering wished less than mine is the same as the sum of all house
to form ranks for a parade. In ranks of 3 abreast, 2 men numbers greater than mine. What is my number and
were left over; in ranks of 5, 4 over; in 7's,6 over; and how many houses are there on my road?
11's, 10 over. What is the least number of marchers
there must have been? House number: 204
Number of houses: 288
1154 marchers
The sum and difference of two squares may be primes:
What is the remainder upon dividing 5^999,999 by 7? 4 – 1 = 3 and 4 + 1 = 5; 9 – 4 = 5 and 9 + 4 = 13, etc.
Can the sum and difference of two primes be squares?
6 If so, how many different primes is this possible?

A pet store offered a baby monkey for sale at $1.25. The p = 2, q = 2

monkey grew. Next week it was offered at $1.89, then
$5.13, then $5.94, then $9.18. What will be the price of In what days of the week can the first day of a century
the monkey on the sixth week? fall? (The first day of the twentieth century was Jan. 1,
1901)
$12.42
Monday, Tuesday, Thursday, and Saturday only
Assume the universe is a billion billion light years in The 21st century will start on a Monday
diameter and is packed solidly with matter weighing a
billion billion tons per cubic inch and each gram of this In the arithmetic of Puevigi, 14 is a factor of 41. What is
matter contains a billion billion atoms. Also, every the base of the number system?
second during the past billion billion years, a billion
billion similar universes were created- Without using 11
any symbols and restricting yourself to a total of three
digits, write a number that far exceeds the total atoms No factorial can end in five zeros. What is the next
of all these universes. smallest number of zeros in which a factorial cannot
end?
9^(9^(9))
11
The sum of the digits on the odometer in my car (which
reads up to 99999.9 miles) has never been higher than Barnie Bookworm bought a thriller - found to his dismay,
Just before the denouement a fascicle astray.
it is now, but it was the same 900 miles ago. How many
Instead of counting one through ten, a standard cure for rages,
miles must I drive before it is higher than it is now. He totaled up the number of the missing sheal of pages.
The total was eight thousand and six hundred fifty-six.
100 miles What were the missing pages? Try to find them just lor kicks

The first expedition to Mars found only the ruins of a Page 225-286
civilization. The explorers were able to translate a
Martian equation as follows: 5x^2 – 50x + 125 = 0, x = The Sultan arranged his wives in order of increasing
5, x = 8. This was strange mathematics. The value x = seniority and presented each with a golden ring. Next,
5 seemed legitimate enough but x = 8 required some every 3rd wife, starting the 2nd, was given a 2nd ring;
explanation. If the Martian number system developed in of every 3rd one starting with the 2nd received a 3rd
a manner similar to ours, how many fingers would you ring, etc. His first and most cherished wife was the only
say the Martians had? one to receive 10 rings. How many wives had the
Sultan.
13 fingers
9,842 wives
A rectangular picture, each of whose dimensions is an
integral number of inches, has an ordinary rectangular The alphametic LIX + LVI = CXV and X^2 = C involving
frame 1 inch wide. Find the dimensions of the picture if Roman numerals is correct. It will still be correct if the
the area of the picture and the area of the frame are proper Arabic numerals are substituted. Each letter
equal? denotes the same digit throughout, and no 2 letters
stand for the same digit. Find the unique solution.
3x10 or 4x6
938
 Chapter 8: More Advanced Problems The price per cubic inch for plantinum trays is the same
A collection of problems from various fields which as that per square inch for platinum sheets. A metal
require calculus or other sophisticated supply house has a square of platinum which will yield
mathematical tools the same amount whether sold as a sheet or fashioned
into a tray of maximum volume with the four cut-out
A ball is dropped from a height of 10 feet. It rebounds corners sold as sheets. How big is the square?
one-half the distance in each bounce. What is the total
distance it travels? 1 foot

30 feet

A rectangular box without a top is to be made from a

sheet of metal in the manner familiar to all calculus
students, i.e., by cutting out squares from the corners
and bending up the sides. The finished product is to
have maximum volume and its dimensions are to be all
integers" How will these dimensions compare if the
metal cutout amounts to 10% of the original sheet?

6:3:1

A student studying series starts with the familiar 1 + 1/2

+ 1/4 + 1/8 + … and inserts terms midway between
these, obtaining 1 + 3/4 + 1/2 + 3/8 + ¼ + … He divides
this by 2, since, as he explains it. “There are now twice
as many terms as before.” He repeats the process,
interpolating terms between those already placed, again
dividing by 2. If he continues this indefinitely, what limit
will the series approach?

3/2

Mr. X veers to the right when he walks. The curvature of

his path is proportional to his latitude. He starts walking
North from point A on the equator, in the area of a large
level plain, and finds he Is proceeding East when he is
one mile north of the equator. He continues walking and
arrives back at the equator at point B. What is the
straight-line distance from A to B?

2x = a trifle less than 1.2 miles

Which contains more terms: the general polynomial of

tenth degree in six variables or the general polynomial
of sixth degree in ten variables?

Both are equal (8,008 terms)

A boat owner agrees to take a group on an outing at

$4.50 apiece if the number of passengers is equal to or
less than his break-even point. For each person above
this he reduces the fare for all passengers 3 cents per
person. If he has on board now the number of
passengers that maximizes the total collected, what is
the boat owner's profit?

Zero
MSTE –TERMS of interest.
a. Octagon
MATHEMATICS, SURVEYING AND b. Circle
TRANSPORTATION ENGINEERING c. Equilateral triangle
d. Rectangle
1. Standard sign shape for STOP sign.
a. Octagon 8. Standard sign shape for pedestrian
b. Circle and school crossing sign.
c. Heart a. Octagon
d. Equilateral triangle b. Pentagon
c. Equilateral triangle
2. Standard sign shape for GIVE WAY d. Rectangle
sign.
a. Octagon 9. It is anything that can cause harm.
b. Circle a. Hazard
c. Equilateral triangle b. Risk
d. Rectangle c. Severity
d. Accidents
3. Standard sign shape for regulatory
signs. 10. It is the probability of harm
a. Octagon actually being done.
b. Circle a. Hazard
c. Equilateral triangle b. Risk
d. Rectangle c. Severity
d. Likehood
4. Standard sign shape for additional
information. 11. It is a violation of an accepted
a. Octagon safe procedure which could permit
b. Circle the occurrence of an accident.
c. Equilateral triangle a. Accident
d. Rectangle b. Risk
c. Unsafe Act
5. Standard sign shape for warning d. Unsafe Condition
signs.
a. Octagon 12. A hazardous physical condition or
b. Circle circumstance which could directly
c. Equilateral triangle permit the occurrence of an accident.
d. Rectangle a. Accident
b. Risk
6. Standard sign shape for directional c. Unsafe Act
signs, roadwork signs, signs for d. Unsafe Condition
special purposes, and supplementary
plates for warning signs. 13. It is advisable for a site plan to
a. Octagon contain a large-scale map of the
b. Circle overall area and to indicate where the
c. Equilateral triangle project is located on the site.
d. Rectangle a. Location Map
b. Site Plan Map
7. Standard sign shape for facility c. Vicinity Map
information signs, instruction signs, d. Google Map
guide signs and destinations of point
14. It provides the detailed road maybe unexpected or
requirements for the materials, hazardous.
equipment and workmanship to be a. Overhead Signs
incorporated into the project. b. Roadwork Signs
a. Specifications c. Warning Signs
b. Bid Documents d. Guide Signs
c. Estimates
d. Plans 20. Signs which warns or advise
temporary hazardous conditions that
15. This drawing has elevation as its could endanger road users or the
vertical axis and horizontal distance men and equipment engaged on
as measured along the centerline of roadworks.
the facility (or other reference line) as a. Overhead Signs
its horizontal axis. b. Roadwork Signs
a. Profile c. Warning Signs
b. Geographic d. Guide Signs
c. Topographic
d. Surface 21. Signs which provide means
of displaying essential traffic
16. Device mounted on a fixed information on wide multi- lane
support (permanent signs) or roads, where some degree of lane
portable support (temporary signs) use control is required or where side
whereby a specific message is of road clearance is insufficient to
conveyed by means of words or accomodate a road side sign.
symbols placed or erected for the a. Overhead Signs
purpose of regulating, warning or b. Roadwork Signs
guiding traffic. c. Warning Signs
a. Roadwork signs d. Guide Signs
b. Traffic signs
c. Overhead signs 22. Signs which inform and
d. Special instruction signs advise road users of directions,
distances, routes and the location of
17. Signs that inform road users of the services for road users and point of
traffic laws and regulations which are interest.
disregarded will constitute an a. Overhead Signs
offense. b. Roadwork Signs
a. Warning Signs c. Warning Signs
b. Regulatory Signs d. Guide Signs
c. Overhead Signs
d. Guide Signs 23. Signs used to guide drivers
through a change in horizontal
18. Signs that instruct road users alignment of the road.
to meet certain traffic rule a. Chevron signs
requirements on road condition. b. Supplementary signs
a. Special Instruction Signs c. Guide signs
b. Regulatory Signs d. Delineators
c. Warning Signs
d. Guide Signs 24. The reaction time used for
road safety design is:
19. Signs which warn road users a. 1.0 sec
of condition on or adjacent to the b. 1.5 sec
 c. 2.0 sec c. Compaction
d. 2.5 sec d. Contraction

25. The speed limit appropriate 30. is an increase in soil

on lower standard expressways. density of a cohesive soil resulting
a. 50 or 60 kph from the expulsion of water from the
b. 60 or 75 kph soil’s void spaces.
c. 90 or 100 kph a. Compression
d. 80 or 90 kph b. Consolidation
c. Compaction
26. Ideal capacity of a road is: d. Contraction
a. 2000 vph
b. 1800 vph 31. Compactor
c. 1400 vph production is based on the following
d. 2500 vph data:
I. Number of paces required
27. Which of these contour II. Width compacted per pass
characteristics is not true? III. Compactor speed
a. Contours on the ground can IV. Compacted lift thickness
cross another. V. Job Efficiency
b. Contours are at the right
angles to the slope. a. I, III, IV and V
c. Contour on the ground b. I, II, IV, and V
closes itself. c. all of the above
d. Contours point upstream. d. II, III, IV and V

28. In the Standard practice of 32. The process of giving natural

measuring vertical or zenith angles, soils enough abrasive resistance
the following practices are of great and shear strength to accommodate
importance: traffic or design loads is called.
I. Be sure the instrument is a. Ground Modification
level b. Dynamic Compaction
II. Sight with the vertical c. Vibroflotation
crosshair d. Surcharging
III. Sight exactly on the target
IV. Sight direct and reverse 33. or placing additional weight
on the soil surface, has long been
Which standard practices are true? used to densify cohesive soils.
a. I only a. Ground Modification
b. I, III & IV only b. Dynamic Compaction
c. I & III only c. Vibroflotation
d. All of the above d. Surcharging

29. is the process of 34. It involves dropping a heavy

increasing the density of a soil by weight from a crane onto the ground
mechanically forcing the soil surface to achieve soil densification.
particles closer together, thereby a. Ground Modification
expelling air from the void spaces in b. Dynamic Compaction
the soil. c. Vibroflotation
a. Compression d. Surcharging
b. Consolidation
35. is the process of supplement other controls and
densifying cohesionless soils by devices necessary to alert motorists
inserting a vibratory probe into the of construction and maintenance
soil. activities or obstructions in the
a. Ground Modification roadway.
b. Dynamic Compaction a. Traffic Cones
c. Vibroflotation b. Delineators
d. Surcharging c. Barriers
d. Flashing Lamps
36. Workers in an excavation be
protected from cave-ins by one of 40. Light retro-reflecting devices
the following methods: mounted at the side of the roadway,
in series, to indicate the roadway
I. Sloping or benching of the sides of alignment.
the excavation. a. Traffic Cones
II. Supporting the sides b. Delineators
of the excavation c. Flexible post or Bollard
by shoring. d. Flashing Lamps
III. Placing a shield between
workers and the sides of the 41. Devices which may be
excavation. conical in shape or tubular shaped
IV. Drying soil to prevent collapsing. are capable of performing
channelization of traffic which may
a. all of the above be set on the surface of the roadway
b. I, II, and IV or rigidly attached for continued use.
c. I, II, and III a. Traffic Cones
d. II, III, and IV b. Delineators
c. Flexible post or Bollard
37. In highway construction, the d. Flashing Lamps
process of cutting down high spots
and filling in low spots of each 42. Roadwork devices
roadway layer is called. consisting of precast concrete
a. Balancing sections, sandbag and others which
b. Grading may be used to guide traffic at the
c. Trimming construction site.
d. Finishing a. Barriers
b. Delineators
38. Highway appurtenances c. Temporary Curbing
designed to prevent vehicular d. Flexible post or Bollard
penetration from the travel way to
areas behind the barrier such as to 43. Device used in place of rigid
minimize damage to impacting cones with a minimum of 450 mm by
vehicles and their occupants, and to 50 mm wide with alternate bands of
reduce the risk of injuries to contrasting color as seen by
pedestrians and workers. approaching traffic for delineation of
a. Traffic Cones traffic.
b. Delineators a. Barriers
c. Barriers b. Delineators
d. Temporary Curbing c. Temporary Curbing
d. Flexible post or Bollard
39. Warning devices used to
44. Means any traffic control 50. An instance of something
device marked on the surface of the happening, an unexpected event or
carriageway used to regulate traffic occurrence that doesn’t result in
or to warn or guide road users. serious injury or illness but may
a. Chevron Signs result in property damage.
b. Delineators a. Accident
c. Lane Line b. Incident
d. Road Markers c. Injury
d. Risk
45. Looking at the possibility of
injury or harm occurring to a person 51. A wave at a point where the
if exposed to a hazard. depth is equal to ½ of the
a. Injury Reports wavelength or greater can be
b. Risk Assessment expressed in terms of the
c. Risk Control parameters of the significant wave.
d. Hazard Identification A. Deep Water Wave
B. Highest Wave
46. Recognizing things which C. Significant Wave
may cause injury or harm to a D. Equivalent Depth Wave
person.
a. Injury Reports 52. A hypothetical wave having
b. Risk Assessment a wave height and period equal to
c. Risk Control average values of the wave height
d. Hazard Identification and period of the largest 1/3 of all
waves in the train as counted in the
47. Introduction of measures order of greater wave height
which will eliminate or reduce the A. Deep Water Wave
risk of a person being exposed to a B. Gravity Wave
hazard. C. Significant Wave
a. Injury Reports D. Equivalent Depth Wave
b. Risk Assessment
c. Risk Control
d. Hazard Identification 53. A maximum wave height
and wave period of the maximum
48. Rule is the guidelines wave height in the wave train.
regarding Personal Protective A. Transitional Wave
Equipment (PPE). B. Highest Wave
a. 1040 C. Significant Wave
b. 1080 D. Equivalent Depth Wave
c. 1070
d. 1090 54. Waves which occur in water
having a depth less than one half of
49. An unexpected event which the wavelength and the influence of
results in serious injury or illness of the bottom changes the form or
an employee and may also result in orbital motion from circular to
property damage. elliptical or near elliptical.
a. Accident A. Shallow Water Wave
b. Incident B. Deep Water Wave
c. Injury C. Significant Wave
d. Risk D. Highest Wave
55. Waves formed by the least height, soon after the time of
frictional drag of wind across the full moon and new moon. These
water surface. tides are called:
A. Shallow Wave a. Spring Tide
B. Transitional Wave b. Flood Tide
C. Significant Wave c. Neap Tide
D. Gravity Wave d. Ebb Tide

56. The pressure against a 62. When the lines connecting

vertical wall due to waves. the earth with the sun and the moon
A. Wave Decay form a right angle, that is the moon
B. Dynamic Pressure is in its quarters, then the actions of
C. Rankines Active Pressure the moon and sun are subtractive,
D. Clapotis and the lowest tides of the month
occur, this is called:
57. The regular periodic rise and a. Neap Tide
fall of the surface of the seas, b. Lunar Tide
observable along their shores. c. Diurnal Tide
a. Wave d. Ebb Tide
b. Tide
c. Period of Wave 63. Owing to retardation of the
d. Current tidal wave in the ocean by frictional
force, as the earth revolves daily
58. Waves generated by around its axis and as the tide tends
storms, which occur outside the to follow the direction of the moon,
area of observation. the highest tide for each location is
a. Swells not coincident with conjunction and
b. Shoal opposition but occurs at some
c. Skewd constant time after new and full
d. Ebb moon. This interval which may
amount to as much as two and a
59. A very long standing wave half days is known as:
on a large but limited body of water a. Diurnal Tide
generally occurring when a storm b. Lunar Tide
dies down after producing a wind c. Age of the Tide
tide. d. Semi-diurnal Tide
a. Seiche
b. Shoal 64. The periodic rise and fall of
c. Ebb sea level in response to the
d. Skewd gravitational attraction of the sun
and moon as modified by the earth’s
60. An instrument use to rotation
measure the intensity of wind. a. Rotational Tides
a. Buchanan’s Scale b. Storm Surge
b. Fibonacci Scale c. Gravitational Tide
c. Beuforts Scale d. Astronomical Tide
d. Antwerp Scale
65. The PPA (Philippine Ports
61. In many parts of the world, Authority) requires that water level
the high waters reach their greatest that guarantees about water depth
height and the low waters at the for safety of the ships berthing on a
 certain ports and harbor, below the
mean lower low water should be 70. It is a type of thermoplastic
equal to: lane marking designed to aid and
a. 0.15m – 0.30m provide motorist with visual, audio,
b. 0.12m – 0.40m and warning on the road.
c. 0.15m – 0.40m a. Chevron markings
d. 0.12m – 0.50m b. Painted median
c. Rumble strips
66. Joints placed in concrete d. Diagonal markings
pavements, which are usually placed
transversely, at regular intervals, to 71. Markings which are placed
provide adequate expansion space on sealed shoulders or other sealed
for the slab to expand when the portions of the road where traffic is
pavement is subjected to an increase not desired.
in temperature. a. Chevron markings
a. Hinge Joint b. Painted median
b. Contraction Joint c. Rumble strips
c. Construction Joint d. Diagonal markings
d. Expansion Joint
72. The time for mixing of
67. Joints placed in concrete ingredients for a concrete cement
pavements, which are usually placed road should be done for at least:
transversely at regular intervals a. 2.5 min.
across the width of the pavement to b. 1.5 min.
release some of the tensile stresses c. 3 min.
that are due to a decrease in d. 2 min.
temperature.
a. Hinge Joint 73. How do you test the
b. Contraction Joint relative consistency of concrete?
c. Construction Joint a. Slump test
d. Expansion Joint b. Water-cement ratio
c. aggregate-cement ratio
68. Joints placed in concrete d. All of the above
pavements, which are usually placed
transversely across the pavement 74. Most important process to
width to provide suitable transition prepare concrete:
between concrete placed at different a. Water-cement ratio
times or on different days. b. Batching
a. Hinge Joint c. Cement-aggregate ratio
b. Contraction Joint d. Admixture
c. Construction Joint
d. Expansion Joint 75. When inside the building,
one may notice unusual sounds
69. Joints placed in concrete and change in the building. What
pavements at right angles to the causes these events?
centerline of the pavement is called: a. Temperature
a. Transverse Joint C. Atoms
b. Longitudinal Joint b. Ductility
c. Construction Joint D. Ions
d. Expansion Joint
76. The basic lane width moving in a specified direction on a
appropriate for national road is given lane or roadway that pass a
. given point during specified unit time.
a. 2.40 m a. Traffic Volume
b. Traffic Density
C. 1.80 m c. Traffic Capacity
b. 3.35 m d. Basic Capacity

D. 5.00 m 82. The ability of a roadway to

accomodate traffic volume. It is
77. Any temporary elevated expressed as the maximum number
platform used for supporting of vehicle in a lane or a road that can
employees or materials or both in pass a given point in unit time.
the course of any construction a. Traffic Volume
works. b. Traffic Density
a. Formworks c. Traffic Capacity
d. Basic Capacity
b. Framing
c. Scaffold 83. The maximum number of
d. Bracing passenger cars that can pass a given
point on a lane or roadway during
78. What are the capacity one hour under the most nearly ideal
requirements for all scaffoldings? roadway and traffic conditions which
a. At least 4 times its own weight can possibly be attained.
b. At least 6 times its own weight a. Possible Capacity
c. At most 4 times its own weight b. Practical Capacity
d. At most 6 times its own weigh c. Traffic Capacity
d. Basic Capacity

79. The number of days final 84. The maximum number of

curing for a concrete cement passenger cars that can pass a given
pavement is done for: point on a lane or roadway during
A. 21 days one hour under prevailing roadway
and traffic conditions.
C. 14 days a. Possible Capacity
B. 12 days b. Practical Capacity
c. Traffic Capacity
D. 18 days d. Basic Capacity

85. The maximum number of

80. It is defined as the number passenger cars that can pass a given
of vehicles per unit distance point on a lane or roadway during
occupying a section of roadway at a one hour without traffic density being
given instant time. so great as to cause unreasonable
a. Density delay, hazard, or restrictions to the
b. Flow driver’s freedom to maneuver under
c. Capacity traffic conditions.
d. Volume a. Possible Capacity
b. Practical Capacity
c. Traffic Capacity
81. The number of vehicles
d. Basic Capacity
 asphalt fills the voids in the mix
86. Cracks approximately at right during hot weather and then exudes
angles to the pavement centerline. out onto the surface of the
These may be caused by shrinkage pavement.
or differential thermal stress of the a. Spalling
asphalt concrete or maybe reflective b. Bleeding or Flushing
cracks. c. Raveling
a. Alligator Cracking d. Abrasion
b. Block Cracking
c. Transverse Cracking 91. Elevation differences
d. Longitudinal Cracking between adjacent slabs at
transverse joints. It is usually the
87. Cracks approximately result of pumping and is a major
parallel to the pavement centerline. source of Portland Concrete
These are caused by poorly pavement structure.
constructed construction joints and a. Spalling
shrinkage of asphalt concrete b. Bleeding
surface. c. Faulting
a. Alligator Cracking d. Raveling
b. Block Cracking
c. Transverse Cracking 92. Localized upward buckling
d. Longitudinal Cracking and shattering of the slabs at
transverse joint or cracks. They can
88. Wearing way of the occur when transverse joints are
pavement surface caused by filled with incompressible solid
dislodging of aggregated particles materials.
and binder. This is usually a result of a. Blowups
insufficient asphalt binder in the mix b. Spalling
or stripping of asphalt from particles c. Raveling
of aggregate. d. Faulting
a. Joint or crack spalling
b. Bleeding 93. The breakdown or
c. Flushing disintegration of slab edges at joints
d. Raveling or cracks, usually resulting in the
loss of sound concrete and the
progressive widening of joint or
89. Progressive disintegration of the
crack.
surface between the wheel paths
a. Joint abrasion
caused by dripping of gasoline or oil
b. Joint spalling
from vehicles.
c. Joint raveling
a. Spalling
d. Joint flushing
b. Bleeding
c. Flushing
94. A series of interconnected or
d. Drip Track Raveling
interlaced cracks caused by fatigue
failure of the asphalt concrete
90. The extruding of bitumen onto the
surface under repeated traffic
pavement surface, causing a
loading.
reduction in skid resistance. It is
a. Alligator Cracking
generally caused by excessive
b. Block Cracking
amounts of asphalt in the mix or low
c. Transverse Cracking
air voids content. It occurs when
d. Longitudinal Cracking
95. Cracks forming large 101. The simplest rail capacity
interconnected polygons, usually problem is that involving rail rapid
with sharp corners or angle. These transit systems. These usually
cracks are generally caused by have the following
characteristics:
hardening and shrinkage of the
i. One-way operation
asphalt and or reflection cracking ii. A common speed profile for all
from underlying layers such as trains. That is, each train traverses each
cement-treated base. section of track at the same speed as
a. Alligator Cracking all other trains; consequently, trains
b. Block Cracking do not overtake or pass one another.
c. Transverse Cracking iii. Common station dwell
d. Longitudinal Cracking times. That is, each train spends
the same amount of time
96. It is the timing of signals in relationship stopped at each station as all
to one another so that vehicles travelling other trains; dwell times may
at a predetermined speed can pass vary from station to station
through the greens of successive signals. iv. A fixed minimum front-to-
a. Speed of progression back time gap between trains.
b. Signal Coordination
c. Offset of the cycle a. I-III
d. Band b. III only
c. II and IV only
97. The speed at which vehicles are
d. All of the above
presumed to travel through coordinated
signal system is known as:
102. There are three basic ways of
a. Speed of progression
resolving crossing conflicts.
b. Signal Coordination
c. Offset of the cycle
d. Band I. Time sharing solutions
II. Space sharing solutions
III. Grade separation solutions
98. The time difference between the
IV. Crossing conflict solutions
beginning and end of through band at
any point is known as:
a. I-III
a. indication
b. III only
b. through band
c. cycle c. II and IV only
d. band width d. All of the above

99. The red, yellow, or green light 103. It is the difference between
that is displayed to driven in a the actual travel time and a given
given movement is called an: segment of a transportation
a. indication system and some ideal travel
b. through band time for that segment.
c. cycle a. Queue Time
d. band b. Travel Time
c. Delay
100. The time required for one d. Service Time
complete sequence of signal
indication is called . 104. The time spent in
a. indication decelerating and accelerating the
b. phase vehicle in opening and closing
c. frequency doors.
d. cycle a. Clearance Time
 b. Dwell Time vertical axis and horizontal distance,
c. Influence Time measured perpendicular to the
d. Bebe Time centerline, as its horizontal axis.
A. Profile
105. Headways such that the B. Plan View
vehicles are just filled at the C. Geometric Cross-Section
maximum load point on the route. D. Topographic
a. Policy Headway
b. Space Headway 110. It refers to establishment of
c. Time Headway horizontal and vertical alignments and
d. Capacity Headway cross-section, based on considerations
such as operating characteristics of
106. Poor construction management vehicles, design standards and drainage.
practices, on the other hand, often result A. Plans
in one or more of the following: B. Topographic
I. Project delays that increase C. Geometric Design
labor and equipment cost and the cost D. Contouring
of borrowed funds.
II. High material costs caused by 111. It refers to the physical or
poor purchasing procedures, inefficient environmental conditions of work or
handling, and/or loss. employment, which substantially comply
III. Increased subcontractor cost with the provisions of these Standards.
and poor contractor- subcontractor A. Approved
relations. B. Health
IV. High insurance costs resulting C. Safety
from material and equipment loss or D. Recognized Hazards
damage or a poor safety record.
V. Low profit margin or a loss on 112. Capacity for two-lane highways
construction volume. ranges from:
A. 1000 to 1500
a. I, II, IV and V passenger car
b. III and IV only equivalents per hour
c. I, IV and V B. 1500 to 2000
d. All of the above passenger car
equivalents per hour
107. The action of flattening poured C. 2000 to 2800
concrete into a smooth, flat layer prior to passenger car
finishing the surface. equivalents per hour
A. Finishing D. 2800 to 3000
B. Smoothing passenger car
C. Plastering equivalents per hour
D. Screeding
113. The primary consideration in the
108. In the measures of congestion of design of geometric cross sections for
highway capacity, what will happen as highways, runways and taxiways is
the density continues to increase? .
A. Minimum rate flow is eventually A. Elevation
reached B. Slope
B. Increase speeds and reduced flow C. Drainage
rate D. Carriageway
C. The point is reached at which
speed declines noticeably 114. requires installing
D. Running speed and traffic flow is aluminum hydraulic or other types of
minimum. supports to prevent soil movement and
cave-ins.
109. This view has elevation as its a. Shoring
 b. Benching excavating the sides of an excavation to
c. Trenching form one or a series of horizontal levels
d. Sloping or steps, usually with vertical or near-
vertical surfaces between levels.
115. If the equal sides of an a. Shielding
isosceles triangle are given, what length b. Shoring
of the third side will provide maximum c. Benching
area? d. Sloping
a. equal to the given sides
b. 𝟐√𝟐 times the length
c. 2 times the length
d. √𝟐 times the length

116. The maximum volume that can

be placed in the bucket without spillage
based on a specified angle of repose for
the material.
a. Heaped Volume
b. Waterline Capacity
c. Bank Volume
d. Struck Capacity

117. Some ways in which productivity

can be increased and costs minimized
during construction include the
following:

i. Good work planning

ii. Carefully selecting and training
workers and managers.
iii. Efficiently scheduling labor,
materials, and equipment
iv. Properly organizing work.
v. Using labor saving techniques,
such as prefabrication and
preassembly.
vi. Minimizing rework through
timely quality control
vii. Preventing accidents through
good safety procedures.

a. I,II, III, VI and VII

b. I, IV, VI, VII
c. I, II, IV, VII
d. All of the above

118. Involves dropping a heavy

weight from a crane onto the ground
surface to achieve soil densification.
a. Dynamic Compaction
b. Soil stabilization
c. Vibratory Compaction
d. Dropping Compaction

119. ________ means a method of

protecting workers from cave-ins by
HGE – TERMS a. Darcy’s Law
b. Stoke’s Law
HYDRAULICS AND PRINCIPLES OF
c. Archimedes’ Principle
GEOTECHNICAL ENGINEERING d. Equilibrium of floating bodies
1. Ratio of volume of voids and volume
10. What is soil in civil engineering?
of soil.
a. Porosity
b. Degree of Saturation a. The material in a relatively thin
c. Void Ratio surface zone within roots occur
d. None of the above b. The unaggregated and
uncemented deposits of minerals
2. Ratio of volume of voids and volume and organic particles covering the
of soil solids. earth’s crust
a. Void Ratio c. The substance existing on the
b. Porosity earths surface, which grows and
c. Degree of Saturation develops plants
d. None of the above d. None of the above

3. Ratio of volume of water and volume 11. Rise of water table above the
of soil. ground surface causes:
a. Degree of Saturation
b. Void Ratio a.Equal increase in pore water
c. Porosity pressure and total stress
d. None of the above b.Equal decrease in pore water
pressure and total stress
4. Which is true for porosity? c.Increase in pore water pressure
a. 0 < n < 100 but decrease in total stress
b. 0 ≤ n ≤ 100 d.Decrease in pore water pressure
c. 0≤n but increase in total stress
d. 0<n
12. The shear strength of a soil:
5. Which is true for void ratio?
a. 0 < e < 100 a.Is directly proportional to the angle
b. 0 ≤ e ≤ 100 of internal friction of the soil
c. 0 ≤ e b.Is inversely proportional to the
d. 0 < e angle of internal friction of the soil
c.Decreases with increase in normal
6. Which is true for stress
degree of saturation? d.Decreases with decrease in
a. 0 < S < 100 normal stress
b. 0 ≤ S ≤ 100
c. 0 ≤ S 13. Effective stress on soil:
d. 0 < S
a. Increases voids ratio and
7. In the unit phase diagram for a decreases permeability.
soil mass: b. Increases both voids ratio
a. The volume of water is taken as and permeability.
unity c. Decreases both voids
b. The total volume is taken as ratio and permeability.
unity d. Decreases voids ratio and
c. The weight of solids is taken as increases permeability.
unity
d. The volume of solids is taken as 14. The coefficient of compressibility of
unity soil, is the ratio of:

8. “Loam” means: a.Stress to strain

a. Silty with little sand b.Strain to stress
b. Sandy silt with little clay c.Stress to settlement
c. Clayey sand exhibiting slight d.Rate of loading to that of settlement
cohesion
d. Mixture of sand, silt, and clay 15. A cohesive soil deposit is
size particles in approximately considered stiff if the unconfined
equal proportions compression strength, in kPa, is between

9. Principle involved in the a. 0 to 25

relationship between submerged unit b. 50 to 100
weight and saturated unit weight of a soil is: c. 100 to 200
 d. 25 to 50 a. center of gravity of the
floating body and the center of
16. A cohesive soil deposit is buoyancy
considered soft if the unconfined b. center of gravity of the
compression strength, in kPa, is between floating body and the metacenter
a. 0 to 25 c. metacenter and the center
b. 50 to 100 of buoyancy
c. 100 to 200 d. original center of buoyancy
d. 25 to 50 and the new center of buoyancy

17. A cohesive soil deposit is 25. The weight per unit volume of a
considered very soft if the unconfined liquid at a standard temperature and
compression strength, in kPa, is between pressure is called:
a. 0 to 25 a. specific weight
b. 50 to 100 b. specific gravity
c. 100 to 200 c. mass density
d. 25 to 50 d. none of the above

18. If the shearing stress is zero on two 26. A pressure surge or wave caused
planes, then the angle between the two when a fluid in motion is forced to stop or
planes is change direction suddenly (momentum
a. 45° change) is referred to in hydraulics as:
b. 135°
c. 90° a. hydraulic jump
d. 225° b. potential head
c. hydrodynamics
19. Compression of soil occurs rapidly d. water hammer
if voids are filled with
a. Air 27. A type of shock where the flow
b. Water undergoes a sudden transition from swift
c. Partly with air and partly with flow to tranquil flow.
water
d. None of these a. water hammer
b. hydraulic jump
20. Cohesionless soil is c. non-uniform flow
a. Sand d. celerity
b. Silt
c. Clay 28. A fluid property that measures the
d. Clay and silt fluid’s resistance to shear stress.
a. viscosity
21. In a triaxial compression test when b. density
drainage is allowed during the first stage c. bulk modulus of elasticity
only and not during the second stage, the d. surface tension
test is known as
a. Consolidated drained test 29. The vena contrata of a
b. Consolidated undrained test circular orifice is ____ approximately
c. Unconsolidated drained test diameter downstream from the inner face of
d. Unconsolidated undrained the orifice plate:
test a. 1/2
b. 1/3
22. Where is the metacenter for stable c. 1/4
equilibrium? d. 2/3
a. above center of gravity
b. at the center of gravity 30. When the ship’s metacenter and
c. below the center of gravity center of gravity coincide at same point
d. one half of the total draft then the vessel is said to be in:
a. equilibrium
23. When the metacenter of a floating b. stable equilibrium
body is lower than the center of gravity, c. unstable equilibrium
then the body will be in? d. neutral equilibrium
a. unstable equilibrium
b. stable equilibrium 31. A force within the surface layer of a
c. neutral equilibrium liquid that causes the layer to behave as an
d. none of the above elastic sheet.
a. celerity
24. The metacentric height is the b. buoyant force
distance between the c. surface tension
 d. capillarity c. steady flow
d. uniform flow
32. In the triaxial test, the deviator
stress increases the shear stress on what 40. Uninterrupted flow in a fluid near a
plane? solid boundary in which the direction of flow at
a. Horizontal plane only every point remains constant:
b. Vertical plane only a. continuous flow
c. Both horizontal and vertical b. laminar flow
planes c. steady flow
d. All planes except the horizontal d. uniform flow
and vertical planes
41. Type of flow where at any time, the
33. Which of the following tests is not discharge or flow rate at every section of the
done on a laboratory set up? stream is the same.
a. Direct shear test a. continuous flow
b. Vane shear test b. steady flow
c. Triaxial test c. critical flow
d. Unconfined compression test d. uniform flow

34. The shear strength of a soil: 42. Type of flow in which, for a fixed rate
a. Increases with an increase in of flow, the specific energy is minimum.
the normal stress a. continuous flow
b. is proportional to the cohesion b. steady flow
of the soil c. critical flow
c. Is generally known as the d. subcritical
strength of the soil
d. All of the above 43. Type of flow in which the density of the
fluid is constant from one point to another.
A. continuous flow
35. Minor losses through valves, B. steady flow
fittings, bends, contractions etc. are C. compressible flow
commonly modeled as proportional to: D. incompressible flow
a. total head
b. static head 44. Type of flow in which the fluid
c. velocity head particles rotate about their own axis while
d. pressure drop flowing along the streamlines.
a. rotational flow
36. The best hydraulic cross section for b. steady flow
a trapezoidal channel of base width b is one c. irrotational flow
for which the length of the side edge of the d. incompressible flow
flow section is:
a. b 45. Which one of the following
b. b/2 statements is not correct?
c. 2b
d. √𝟑𝐛 a. Specific energy is the total energy
above the floor of an open channel
37. When the path lines of the individual b. For a given specific energy, two
particles of a flowing liquid are irregular depths exist and these are called
curves and continually cross each other alternate depths
and form a complicated network, the flow is c. Velocity of flow is critical at
called: maximum specific energy
a. uniform d. Critical velocity occurs at Froude
b. laminar number = 1
c. continuous
46. All other conditions and parameters
d. turbulent
remaining the same, water hammer
pressure can be reduced by
38. Type of flow where the flow rate
does not change over time.
a. continuous flow a. using pipe of greater diameter
b. laminar flow b. using pipe of greater wall thickness
c. steady flow c. using a more elastic pipe
d. uniform flow d. increasing the velocity of the
pressure wave
39. Type of flow where the mean
velocity of flow for a given length or reach is the 47. If a water tank, partially filled with
same at every cross section. water is being carried on a truck, moving
a. continuous flow with a constant horizontal acceleration, the
b. laminar flow level of liquid will
 a. rise and fall alternately on the front
side of the tank 55. The soil which contains finest grain
b. fall on the rear side of the tank particles, is
c. remain the same on both side of the a. Coarse sand
tank C.
d. rise on the rear side and fall on the Silt
front side of the tank b. Fine sand
D.
48. As the depth of immersion of a Clay
vertical plane surface increase, the location
of center of pressure 56. If the plasticity index of a soil mass is
zero, the soil is
a. comes closer to the center of gravity a. Sand
of the area C.
b. moves apart from the center of Clay
gravity of the area b. Silt
c. ultimately coincides with the center D.
of gravity of the area Clayey silt
d. remains unaffected

49. In open channel water flows under 57. Volume change in saturated soils caused
a. force of gravity by the expulsion of pore water from
b. atmospheric pressure loading?
c. hydrostatic pressure a. Initial Consolidation
d. mechanical pressure b. Primary Consolidation
c. Secondary Consolidation
50. The pressure exerted onto a liquid d. None of the above
is transmitted undiminished to all portions
of the liquid. This principle in fluid 58. The neutral stress in a soil mass is
a. Force per neutral area
mechanics is attributed to:
b. Force per effective area
a. Archimedes
b. Boyle c. Stress taken up by the pore water
c. Torricelli d. Stress taken up by solid particles
d. Pascal
59. Negative skin friction on piles.
51. In any stream flowing steadily a. Is caused due to relative settlement
without friction, the total energy contained of the soil
is the same at every point in its path of flow. b. Is caused in soft clays
This principle is attributed to: c. Decreases the pile capacity
a. Torricelli d. All of the above
b. Bernoulli
c. Pascal 60. If the ground water table in a soil
d. Boyle formation rises as resulting of flooding, the
bearing capacity of the soil:
52. The volume of a gas at constant a. Increases
temperature varies inversely as the b. Unaffected
pressure applied to the gas. This principle c. Decreases
d. Depends on the footing load
is attributed to:
a. Boyle
b. Pascal 61. One of the following foundation conditions
c. Archimedes does not affect the bearing capacity of the
d. Bernoulli supporting soil.
a. Unit weight of the soil
53. If the volume of voids is equal to the b. Depth of the founding of footings
volume of solids, what is the porosity and c. Load imposed onto the soil
void ratio equal to? d. Position of ground water table
a. 0 and 1
b. 1and 0 62. A decrease in water content results in a
c. 1 and 0.5 reduction of the volume of soil in:
d. 0.5 and 1 a. Liquid state
b. Plastic state
54. A process by which water-saturated soil c. Semi-solid state
sediment temporarily loss strength and acts d. All of these
as a fluid.
a. Consolidation 63. The water content in a soil sample when it
C. Settlement continues to loose weight without loosing
b. Plasticity the volume,is called
D. Liquefaction a. Shrinkage limit
 b. Plastic limit b. the hydraulic radius must be equal
c. Liquid limit to half the depth of flow
d. Semi-solid limit c. the semicircle drawn with top width
as diameter must touch the three
64. When the plastic limit of a soil is greater sides of the channel
than the liquid limit, then the plasticity index d. All of these
is reported as :
a. Negative 72. A cohesionless soil is considered
b. Zero dense if the SPT “N” value is between
c. Non-plastic (NP) A. 0 to 4
d. 1
C. 30 to 50
65. The continuity equation is based on the B. 10 to 30
principle of:
a. conservation of mass D. 4 to 10
b. conservation of momentum
c. conservation of energy 73. A cohesionless soil is considered loose if
d. conservation of force the SPT “N” value is between
A. 0 to 4
66. When a valve is suddenly closed on a
liquid flowing through a long pipe, the C. 30 to 50
pressure wave of high intensity thus B. 10 to 30
generated is known as:
a. water hammer D. 4 to 10
b. pressure wave
c. flow hammer
74. A cohesionless soil is considered
d. jet hammer
very loose if the SPT “N” value is between
A. 0 to 4
67. Which property of the fluid accounts for
the major losses in pipes? C. 30 to 50
a. density B. 10 to 30
b. specific gravity
c. viscosity
D. 4 to 10
d. compressibility
75. Soil grains with particle size greater than
68. An open vessel of water is accelerated up
4.75 mm but less than 75 mm according to
an inclined plane. The free water surface
USCS.
will
a. Cobbles
a. be horizontal
C. Boulder
b. make an angle in direction of b. Gravel
inclination of inclined plane
c. make an angle in opposite D. Sand
direction to inclination of inclined
plane 76. Soil grains with particle size is greater
d. any one of above is possible than 75 mm according to USCS.
a. Cobbles
69. The horizontal to vertical side slope in
case of Cipolletti weir? C. Boulder
a. 1:1 b. Gravel
b. 1:4
c. 1:2 D. Sand
d. 4:1
77. The maximum shear stress occurs on the
70. The horizontal component of the force filament which makes an angle with the
on a curved surface is equal to horizontal plane equal to:
a. weight of liquid vertically below the a. 30°
curved surface
b. force on a vertical projection of the C. 60°
curved surface b. 45°
c. product of pressure at its centroid
and the area D. 90°
d. weight of liquid retained by the
curved area 78. A practice of procedure used to asses the
particle size distribution (also called
71. For the most economical trapezoidal gradation) of a granular material. The size
open channel, distribution is often of critical importance to
a. half of the top width must be equal the way the material performs in use.
to one of the sloping sides a. Consolidation test
b. Standard penetration test
 c. Unconfined compression test 87. The over consolidation ratio (OCR) of a
d. Sieve Analysis normally consolidated soil is:
a. Less than 1
79. The average/equivalent coefficient of b. Equal to 1
permeability of natural deposits c. Greater than 1
a. Parallel to stratification is always d. None of the above
greater than that perpendicular to
stratification 88. Pick up the correct statement from the
b. Parallel to stratification is always following:
less than that perpendicular to a. Failure plane carries maximum
stratification shear stress
c. Is always same in both directions b. Failure plane does not carry
d. Parallel to stratification may or may maximum shear stress
not be greater than that c. Failure plane carries shear stress
perpendicular to stratification equal to maximum shear stress
d. None of these
80. Transporting and re-depositing soils, is
done by 89. At liquid limit a soil has
a. Water a. No shearing strength
b. Glacier b. Negligible or very small shear
c. Gravity strength
d. All the above c. High shearing strength
d. Nothing to do with shearing
strength.
81. Residual soils are formed by
a. Glaciers
b. Wind 90. A theorem in fluid dynamics relating the
c. Water speed of fluid flowing out of an orifice to the
d. None of the above height of fluid above the opening.
a. Archimedes
82. Textural classifications are merely based b. Pascal
c. Torricelli
on:
a. Grain size d. Bernoulli
b. Consistency limits 91. Gauge pressure is
c. Grain size and consistency limits a. absolute pressure - atmospheric
d. Plasticity index pressure
b. absolute pressure + atmospheric
83. The minimum number of observation pressure
wells required to determine the c. atmospheric pressure - absolute
permeability of a stratum in the field by a pressure
pumping test is: d. none of these
a. One
b. Two 92. In flow, the liquid particles may possess
c. Three a. potential energy
d. None of the above b. kinetic energy
c. pressure energy
84. Consolidation is a fuction of.. d. all the above
a. Function of the total stress.
b. Function of the neutral stress. 93. For most economical rectangular section
c. Function of the effective stress. of a channel, the depth is kept
d. Does not depend upon the present a. one-fourth of the width
stress. b. three times the hydraulic radius
c. half the width
85. Allowable bearing pressure for a d. none of these
foundation depends upon:
a. Allowable settlement only 94. An index used to identify the swelling
b. Ultimate bearing capacity of soil potential of clay soils is called
only a. Plasticity Index
c. Both allowable settlement and b. Liquidity Index
ultimate bearing capacity c. Consistency Index
d. None of the above d. Activity

86. The over consolidation ratio (OCR) of an 95. The property of a soil which permits
over consolidated soil is: water to percolate through it
a. Less than 1 a. Moisture content
b. Equal to 1 b. Permeability
c. Greater than 1 c. Capillarity
d. None of the above d. None of these
96. Which of the following methods is best c. lesser than static pressure
suited for determination of permeability of d. none of these
coarse-grained soils?
a. Constant head method 104. Falling drops of water become
b. Falling head method spheres due to
c. Both the above a. adhesion
d. None of the above b. cohesion
c. surface tension
97. Terzaghi's bearing capacity factors Nc, d. viscosity
Nq and Nγ are functions of
a. Cohesion only 105. For a long pipe, the head loss
b. Angle of internal friction only a. at the entrance is ignored
c. Both cohesion and angle of internal b. at the outlet is ignored
friction c. at the entrance and outlet both are
d. None of the above ignored
d. due to friction is ignored
98. Coefficient of earth pressure at rest is
a. Less than active earth pressure but 106. If cohesion between molecules of a
greater than passive earth fluid is greater than adhesion between fluid
pressure and glass, then the free level of fluid in a
b. Greater than active earth pressure dipped glass tube will be
but less than passive earth a. Higher than the surface of liquid
pressure b. The same as the surface of liquid
c. Greater than both the active earth c. Lower than the surface of liquid
pressure and passive earth d. Unpredictable
pressure
d. Less than both the active and 107. Coefficient of velocity is defined as
passive earth pressures the ratio of
a. Actual velocity of jet at vena
99. Atmospheric pressure varies with contracta to the theoretical velocity
a. altitude b. Area of jet at vena contracta to the
b. temperature area of orifice
c. weather conditions c. Actual discharge through an orifice
d. all of the above to the theoretical discharge
d. None of the above
100. The rise of the liquid along the walls of a
revolving cylinder above the initial level, is 108. When a cylindrical vessel
a. greater than the depression of the containing liquid is resolved, the surface of
liquid at the axis of rotation the liquid takes the shape of
b. lesser than the depression of the a. A triangle
liquid at the axis of rotation b. A paraboloid
c. the same as the depression of the c. An ellipse
liquid at the axis of rotation d. None of these
d. none of these
109. The locus of elevations to which
101. The specific weight of water is liquid successive piezometer tubes to any
1000 kg/m3 selected datum is known as.
a. at normal pressure of 760 mm a. Hydraulic gradient
b. at 4°C temperature b. Energy head
c. at mean sea level c. Hydraulic head
d. all the above d. Energy gradient

110. They are used to measure pressure

102. The width of a weir w heads in pipes where the liquid is in motion.
ith end contraction, is a. Manometer
a. equal to the width of the channel
b. Venturi meter
b. less than the width of the channel
c. Pitot tube
c. half the width of the channel
d. none of these d. Piezometer

103. An open container filled with water 111. The difference between energy
is moved vertically upward with a uniform gradient and hydraulic gradient is called.
linear acceleration. The pressure at its a. Elevation head
bottom will be b. Pressure head
a. greater than static pressure c. Velocity head
b. equal to static pressure d. Energy head
112. Minimum specific energy of an open rectangular channel with critical depth dc.

a. (1/2)dc C. (2/3)dc
 b. (1/3)dc D. (3/2)dc
113. Which of the following does not describe real fluids.
a. Infinite viscosities
b. Non-uniform velocity distribution
c. Incompressible
d. Experience friction and turbulence

114. The section on the jet where the contraction ceases is called the:
a. vena contracta
b. vena cava
c. vena contrata
d. vena canton

115. It is the speed at which the surge (or wave) is moving with respect to fluid medium.
a. velocity of flow C. surge
b. water hammer D. celerity
 ● Fine Aggregate - (19 mm > 4.75 mm) passes ¾in (19 mm) sieve and retains No. 4
HGE - TERMINOLOGIES (4.75 mm) sieve.
MAY 2015 ● Location of GWT, depth of backfill and plasticity of soil affects the settlement of
● Surface Tension - the elastic tendency of liquids which makes them acquire the least footing.
surface area possible. It is responsible, for example, when an object or insect such as ● Steepness of the fill and steepness of the cut shall not exceed to 1:2 (1 vertical and 2
mosquitoes that is denser than water is able to float or run along the water surface. horizontal).
● Degree of Saturation - the ratio between the volume of water and the volume of voids. MAY 2016
● Porosity - the ratio between the volume of void and the volume of the soil mass. ● Turbulent - when the path lines of the individual particles of a flowing liquid are irregular
● Moisture Content - the ratio between the weight of water and the weight of solid curves and continually cross each other and form a complicated network.
particles. ● Hydraulic gradient - a line joining the points of highest elevation of water in a series of
NOVEMBER 2015 vertical open pipes rising from a pipeline in which water flows under pressure.
● Archimedes - states the law of buoyancy. ● Water Hammer - a pressure surge or wave caused when a fluid in motion is forced to
● Steady Flow - a flow in which the velocity of the fluid at a particular fixed point does not stop or change direction suddenly (momentum change) is referred to in hydraulics.
change with time. ● 0 to 24 - a cohesive soil deposit is considered soft if the unconfined compression
● Cohesion - is the component of shear strength of a rock or soil that is independent of strength in kPa.
interparticle friction. NOVEMBER 2016
● Liquefaction - a phenomenon in which the strength and stiffness of a soil is reduced by ● 4 C° - temperature at which liquid water has the highest density.
earthquake shaking or other rapid loading. ● Pascals - a principle of mechanics that the pressure exerted onto a liquid is transmitted
● Effective Stress - a pile of sand keeps from spreading out like a liquid because the equally and undiminished to all portions of the liquid.
weight of the sand keeps the grains stuck together in their current arrangement, mostly ● Bernoulli - a principle that in any stream flowing steadily without friction the total energy
out of static friction. This weight and pressure called… contained is the same at every point in its path of flow.
● Gas - not a soil component. (Note: Components of soil are organic materials, minerals, MAY 2017
etc.) ● Porosity - the ratio between the volume of void and the volume of the soil mass.
● Sieve Analysis - a practice procedure used to assess the particle size distribution (also ● Degree of Saturation - the ratio between the volume of water and the volume of voids.
called gradation) of a granular material. The size distribution is often called of critical ● No. 40 - for determining the atterberg limit which is the plastic and liquid limits, the soil
importance to the way the material performs in use. sample must pass through 0.425 mm sieve.
● Gravel - according to USCS, is a soil grain with grain size greater than 4.75 mm but less NOVEMBER 2018
than 75 mm. (75 mm > 4.75 mm) ● Easy to compact, high shear strength and prone to settlement due to vibrating
● Boulders - particles of rock will not pass a 12 in (200 mm). (200 mm < …) load are the characteristics of cohesionless soil.
● Cobble - particles of rock that will pass a 12in (300 mm) square opening and be retained ● In standard penetration tests, medium dense sand has a number of blows of 10 to 30.
on a 3in (75 mm). (300 mm > 75 mm) APRIL 2023 (Bessavilla)
● Coarse Aggregate - (75 mm > 19 mm) passes 3in (75 mm) sieve and retains ¾in (19 ● The shear strength of a soil increases with increase in normal stress.
mm) sieve. ● Triaxial shear test acts on all plane axes except x and y axis.
 ● In what plan is the additional stress (deviator stress) can affect the shear stress? ● Work hardening - is the strengthening of a metal by plastic deformation.
Horizontal ● Buckling - failure by lateral or torsional instability of a structural member, occurring with
● Vane Test is a test not performed in a laboratory. stresses below the yield of ultimate values.
● In AASHTO, soil greater than 75mm is classified as cobbles. MAY 2016
● In 1.3cNc + qNq + 0.4BɣNɣ, Nc, Nq and Nɣ are function of angle of friction. ● Toughness - the ability of the material to absorb energy in the plastic range.
● When molecules get attracted to others it is called cohesion. ● Resilience - the ability of material to absorb energy in the elastic range.
● Where is the metacenter for stable equilibrium? Above center of gravity. ● Ductility - refers to the ability of a material to deform in the plastic range without
● If the volume of voids is equal to the volume of solids, what is the porosity and void equal breaking
to respectively? 0.5 and 1.0 ● Center of Rigidity - it is the point through which the resultant of the resistance to the
● The shear strength of a cohesionless soil is proportional to the tangent of the angle applied lateral force acts.
of shearing resistance. ● Shear Wall - the point on a structure where the resultant vertical force acts.
● The intensity of vertical stress at a depth due to a point load acting on the surface of a ● Eccentricity - the distance between the center of mass and center of rigidity.
semi infinite elastic soil mass is directly proportional to the square of depth. NOVEMBER 2016
● When the metacenter of a floating body is lower than the center of gravity, then the body ● Ground Motion or Ground Displacement - it is measured by a seismometer.
will be in unstable equilibrium. ● Inverse Stiffness - refers to the flexibility of a structural system.
● The metacentric height is the distance between the center of the gravity of the floating ● Yielding - the stress point where a material will have appreciable deform when a small
body and the metacenter. amount of stress is experienced.
● Negative skin friction on piles caused by soft clay, decreases the pile capacity and ● Toughness - the ability of the material to deform in plastic rance without breaking.
due to relative settlement of soil. ● Elastic Limit - the greatest stress that can be applied to an elastic body without causing
● Specific weight of liquid does not vary on any other planet. permanent deformation.
● In civil engineering, soil is a structural material or uncemented aggregate. NOVEMBER 2017
● The weight per unit volume of a liquid at a standard temperature and pressure is called ● Torsional Shear Stress - the center of mass and center of rigidity of a structure does
specific weight. not coincide; it will develop this kind of stress.
PSAD - TERMINOLOGIES ● Soft Storey - a building which has a floor which is less than 70% as stiff as the floor
MAY 2015 immediately above it, or less than 80% as stiff as the average stiffness of the three floors
● Orthotopic Material - the material composition is the same but its mechanical properties above it.
are different in every direction. ● Storey Drift - refers to the lateral displacement of one level relative to the other level
● Homogeneous - materials are the same at all points in the body. above or below.
● Isotropic Material - has a stress-strain relationship that is independent of the orientation MAY 2018
of the coordinate system at a point. ● Reciprocal of Deflection - best refer to the rigid structure.
● Elasticity - Refers to the tendency of solid materials to return to their original shape after ● Liquefaction is best described as a sudden drop of shear strength.
forces are applied on them. When the forces are removed, the object will return to its ● k = k1 + k2 - If two springs with sudden stiffness of k1 and k2 are arranged in parallel.
initial shape and size. ● Center of Rigidity - the point through which the resultant of the resistance to the
● Yielding - refers to the stress at which a material begins to deform plastically. applied lateral force acts.
 ● Center of Mass - the point o a structure through which the applied seismic force acts. location of services such as gas stations, rest areas, hospitals, and hotels. They are
● Reciprocal of Stiffness - refers to the flexibility of a structure. usually placed on highways, expressways, and other major roads to help drivers
navigate and plan their trips. Guide signs are typically rectangular in shape and have
MSTE - TERMINOLOGIES white lettering on a green or blue background.
MAY 2019 ● Traffic instruction sign is a type of traffic sign used to provide information, guidance or
● Traffic Signs - device mounted on a fixed support whereby a specific message is instructions to road users. These signs are typically used to indicate speed limits,
conveyed by means of words or symbols for the purpose of regulating, warning and direction of travel, lane usage, parking regulations, and other traffic regulations. Traffic
guiding traffic. instruction signs are usually rectangular in shape and are designed with bold,
● Road Work Signs - warn or advise of temporary hazardous conditions that could easy-to-read lettering and symbols to convey their message clearly and quickly to
endanger road users or the men and equipment engaged on roadwork. drivers. They are an important component of traffic control systems and help to ensure
● Special Instructions Signs - signs that instruct road users to meet certain traffic rule safe and efficient traffic flow.
requirements or road condition. ● 7 Ways to avoid traffic conflicts: Separating traffic, Traffic signals, Rounabouts,
● Significant Wave - defined as the average height of the highest one third of waves in a Grade Separations, Speed Limits, Proper signage and markings, Education and
wave train. It is the maximum height and wave period of the maximum wave height in Awareness
wave train. ● Delay - the difference between the actual time and some ideal travel time for a given
● Seiches - are typically caused when strong winds and rapid changes in atmospheric segment of a transportation system.
pressure push water from one end of the body of a water to the other. ● Queue Time - refers to the time a vehicle spends waiting in a queue such as in traffic or
● Wind swells - are created by the wind blowing above the ocean close to the shore. at a toll booth.
● Wake effect - the wind speed decreases and the turbulence increases. ● Transverse Cracks - cracks approximately at right angles to the pavement of centerline
● Wind Sea - when directly generated and affected by local wind. which may be caused by shrinkage or differential thermal stress of the asphalt concrete
NOVEMBER 2019 or may be reflective cracks.
● A caisson is a watertight structure that is used to carry out construction or repair work in ● Alligator Crack - type of cracking caused by a combination of factors such as aging,
the water, particularly in the construction of bridges, dams, and other large structures. It poor drainage, heavy traffic loads and inadequate pavement thickness.
is a box-like structure made of reinforced concrete or steel that is open at the bottom and ● Block Crack - type of pavement distress that appears as interconnected rectangular
closed at the top. cracks resembling a block pattern. It is caused by the shrinkage of the asphalt concrete
● Shoring is a temporary support system used in construction to provide temporary surface.
structural support to an existing structure or excavation. It is typically used to prevent ● Longitudinal Crack - cracks that run parallel to the direction of traffic flow or the
collapse or instability during construction work, such as excavation, demolition, or pavement centerline.
renovation of a building. ● Provision of safety sight distance depends on the characteristics of the road environment
● Pier refers to a raised platform or structure that extends out over a body of water, such such as road geometry, road surface conditions, road illumination at night and
as a river, harbor, or ocean, and provides a docking point for ships to load and unload road topography.
cargo or passengers. ● Provision of safety distance depends on the characteristics of vehicles such as eye
● The sign being described is called a "Guide sign". Guide signs are used to provide height of the driver and type of vehicles.
information to road users about routes, directions, distances, points of interest, and the
 ● Screeding - process of leveling a layer of concrete, mortar or other material with a ● Hardness - a measure of material's ability to resist indentation or penetration.
straight edge of screed board. ● Consolidation - an increase in soil density of a cohesive soil resulting from the
● Trowelling - used in concrete construction to smooth and level the surface of freshly expulsion of water from the soils void spaces.
poured concrete. ● Chronological order of finishing standard weight concrete slabs: Bleeding, Screeding,
● Floating - typically done after the initial screeding process to remove any surface Leveling, Edging, Jointing, Floating, Troweling and Broom Finishing
imperfections and consolidate the concrete surface. ● Elements to consider when planning National Roads:
● Finishing - final stage in which the surface of the concrete is treated to achieve the 1. Limited frontage access
desired appearance, texture and durability. 2. Development set well back from the highway
● Age of tides - it is the interval which may amount to as much as 2.5 days between the 3. All access to premises provided via provincial roads
highest tide for each location and new/full moon. 4. Number of intersections to be minimized
● Diurnal Tide - tidal pattern characterized by a single high tide and single low tide which 5. Suitable at grade-channelized intersections for minor flows and other elements
last 24 hours and 50 minutes. 6. No roadside vendors
● Lunar Tide - refer to the regular rise and fall of sea levels caused by the gravitational ● Health and Safety Committee - given the authority to review reports of inspection,
pull of the Moon on the Earth's ocean. accident investigations and implementation of the program.
● Semi-Diurnal Tide - refer to a pattern of tidal fluctuations characterized by two high ● Grouting - the process of injecting any agent into soil or rock to increase its strength or
tides and two low tides approximately equal size in a 24 hour period. stability, protect foundations or reduce ground water.
● Raveling - wearing way of the pavement surface caused by dislodging of aggregate ● Every construction project shall have a suitable Construction Safety and Health
particles and binder. Program, which must be in accordance with these rules and other orders and issuances
● Bleeding - is a form of distress in asphalt pavement characterized by the upward issued by the DOLE.
movement of asphalt binder in the pavement surface.
● Flushing - is the occurrence of a film of asphalt binder on the pavement surface, caused
by excessive application of a low viscosity asphalt emulsion or an asphalt binder.
● Joint Crack Spalling - is the deterioration or breaking of concrete joints or cracks to the
effect of traffic loading, temperature changes and freeze-thaw cycles. PSAD (Keywords for Problems)
● Batching - is the most important process to prepare concrete. The process of Steel Design
proportioning the cement, water, aggregates and additives prior to mixing concrete. ● Bolts
● Admixture - is a material added to concrete in addition to cement, water and aggregates ○ Maximum safe load - used least value of P.
during the mixing process. ○ Required Diameter - used larger value of stress
● Slump Test - used to determine relative consistency of concrete. ● Retaining Wall
● Water-Cement Ratio - important factor in determining the strength and durability of ○ Minimum thickness - used the larger value
concrete. ○ Maximum thickness - used least value.
● Construction Specifications - written instructions that detail how a facility is to be ● Columns
constructed. ○ Allowable Load - used highest value slenderness ratio or used lowest value of
APRIL 2023 radius of gyration.
○ Moment of Inertia (x axis) - used the distance along y axis
○ Moment of Inertia (y axis) - used the distance along x axis