Abra State Institute of Sciences and Technology

Bangued Campus, Bangued Abra

ENGINEERING DEPARTMENT
CIVIL ENGINEERING LICENSURE EXAM REVIEW
ALGEBRA
REVIEW PROBLEM SET NO. 1

1. Find the Least Common Multiple (LCM) of 96,160, 224, and 352…
a. 1,211,105,280 c. 302,776,320
b. 605,552,640 d. None of the above
2. Find the Greatest Common Factor (GCF) of 1140, 2394, 1596, 1710.
a. 38 c. 82
b. 57 d. None of the above
3. Which of the following is true?
a. √ −2 x √ −2=0 c. √ 10= √ 5+ √ 2
b. 24=4 √ 6 d. 55 +55 +55 +55 +5 5=56
4. Solve for x: 1− √ 1−x=1−√ x
√
a. -16/25 c. -25/16
b. 25/16 d. 16/25
5. √ √
Solve for x if x= 1− 1− √ 1−…
a. 0.723 c. 0.852
b. 0.618 d. 0.452
x y y −x
6. Find in the following equations: 27 =9 , 81 3 =243
a. 2.5 c. 1
b. 2 d. 1.5
7. What is the greatest common factor between the numbers 84. 105, and 2310?
a. 21 c. 14
b. 7 d. 3
2
8. If f ( x )=x + x +1, then f ( x )−f ( x−1 )=?
a. 0 c. 2x
b. X d. 3
9. When (x+3)(x-4) + 4 is divided by (x-k), the remainder is k. find the value of k
a. 4 or 2 c. 4 or -4
b. 2 or -4 d. -4 or -2
2
10. Find the value of k in the equation 4 x + kx+1=0 so that it will only have one real root.
a. 1 c. 3
b. 2 d. 4
11. If 1/x= a + b and 1/y =a -b, then x-y = ?
a. -1/2 a c. -2a/(a 2−b2 ¿
b. -1/2b d. -2b/(a 2−b2 ¿
12. The arithmetic mean of 80 numbers is 55. If two umbers namely 250 and 850 are removed, what is the arithmetic mean of
the remaining numbers?
a. 42.31 c. 50
b. 57.12 d. 38.62
13. If 1/a: 1/b: 1/c=2:3:4, then (a+b+c): (b+c) is equal to
a. 13: 7 c. 10:3
b. 15:6 d. 7:9
14. Find the mean proportional to 5 and 20.
a. 10 c. 12
b. 8 d. 14
15. Find the mean proportionof7, 12 and 21.
a. 36 c. 32
b. 34 d. 14
16. Solve for x: log 6 + x log 4+ log 4 + log (32 +4)
a. 1 b. 2
 c. 3 d. 4
17. If log 5.2 1000=x , what is the value of x.
a. 4.19 c. 3.12
b. 5.23 d. 4.69
18. If log 2 =x and log 3 =y, find log 1.2
a. 2x +y c. 2x + Y-1
b. 2xy/10 d. xy-1
19. Evaluate log 6 845
a. 4. 348 c. 3.761
b. 6.348 d. 5.912
16
1
20. Find the 6th erm of the expansion of
( 2a
−13 )
−22113 −22113
a. c.
256 a11 128 a11
−66339 −66339
b. d.
128 a11 256 a11
12
2
21. The coefficient of the term involving x 9
in the expansion of
( x 2−
x )
a. 25434 c. 25344
b. 52344 d. 23544
22. The sum of the coefficients in the expansion of ( x + y−z )8
a. Less than 2 c. From 2 to 5
b. Above 10 d. From 5 to 10
23. In the equation 3 x 2+ 4 x +(2 h−5)=0, find h if the product of the roots is 4.
a. -7/2 c. 17/2
b. -10/2 d. 7/2
24. Two engineering students are solving a problem leading to a quadratic equation. One student made a mistake in the
coefficient of the first-degree term, got roots of 2 and -3, the other student made a mistake in the constant term, got roots
od -1 and 4. What is the correct quadratic equation?
a. x 2−6 x−3=0 c. x 2−3 x+ 6=0
b. x 2+ 6 x+3=0 d. x 2+ 3 x −6=0
25. Two times the father’s age more than six times his son’s age. Ten years ago, the sum of their ages was 44. The age of the
son is
a. 49 c. 20
b. 15 d. 18
26. The ages of the mother and her daughter are 45 and 5 years, respectively. How many years will the mother be three times
as old as her daughter?
a. 5 c. 15
b. 10 d. 20
27. Two thousand (2000) kg of steel containing 8% nickel is to be made my mixing a steel containing 14% nickel with another
steel containing 6% nickel. How much of the steel containing 14% nickel is needed?
a. 1500 c. 750
b. 800 d. 500
28. Two circles are tangent to a third circle internally and are tangent to a third circle internally. The distances between their
centers are 10m, 13m and 19m. find the radius of the largest circle.
a. 21cm c. 11 cm
b. 25 cm d. 15cm
29. What time between 2 and 3 o’clock will the angle between the ahnds of the clock be dissected by the line connecting the
center of the clock and 3 o’clock?
a. 2:21:27 c. 2:23:54
b. 2:18:46 d. 2:10:54
30. A man left his home at past 3 o’clock P.M. as indicated in his wall clock. Between two to three hours after, he returned
home and notice that the hands of the clock interchanged. At what time tis he left his home?
a. 3:33:47 c. 3:32:47
b. 3:31:47 d. 3:34:47
31. How much water must be added to 1.45 liters, 80 proof liquor to make it 65 proof?
a. 0.29 L c. 0.38 L
b. 0.33 L d. 0.42 L
32. A container is filled with 20 gallons of pure water. Five gallons of water is taken from the container and is replaced by 5
gallons of pure acid then thoroughly mixed. Another 5 gallons is taken from the mixture and is replaced again by 5 gallons
of pure acid. If this process is done repeatedly, find the amount of water in the container after doing the process three
times.
a. 8.75 gal c. 8.44
b. 11.25 gal d. 11.56
33. Two cars run toward each other. Their speeds are 30 kph and 40 kph. At the moment when they are 105 km apart, a bee
flies at 50 kph from the bumper of the slower car to the bumper of the other and shuttles back and forth until the two
vehicles collide. Find the total distance traveled by the bee.
a. 75 km c. 90 km
b. 85 km d. 100 km
34. A man walks from his house to the office. If he leaves at 8:00 A.M. and walk at the rate of 2 kph, he will arrive 3 minutes
earlier, but if he leaves at 8:30 A.M. and walk at 3 kph, he will arrive 6 mins late. What time should he arrive at the office?
a. 9:06 A.M. c. 8:54 A.M.
b. 9:12 A.M. d. 8:43 A.M.
35. A steelman can saw a piece of bar into 5 pieces in 16 mins. In how many minutes can the steelman saw the same bar into
10 pieces?
a. 30 minutes c. 34 minutes
b. 32 minutes d. 36 minutes
36. A swimming pool is filled trough its inlet pipe and then emptied through its outlet pipe in a total of 8 hours. If water enters
through its inlet and simultaneously allowed to live though its outlet, the pool is filed in 7 ½ hours. How long will it take to
fill the pool with the outlet closed?
a. 2.5 hours c. 3.5 hours
b. 3 hours d. 3.75 hours
37. A retired government employee invested P25,000 of his retirement ay at 16% per annum. He found another investment
opportunity at 20% per annum where he invested the rest of his retirement pay. If he realized a total yearly income of 19%
on his two investments, what was his retirement pay?
a. P100,000 c. P96,000
b. P75,000 d. P125,000
38. A man is thinking of buying chocolates, nougats, and candies. Chocolates cost P10.00 a piece, nougats for P1.00 per 3
pieces, and candies for P2.00 per 7 pieces. He wants to buy variety of 100 pieces of these items enough for his budget of
P60.00. How many nougats must he buy?
a. 54 c. 48
b. 42 d. 60
39. In a certain group of customers, each one may drink beer, and/or brandy, and/or whisky, or all. Also, 173 drink beer, 155
drink brandy, 153 drink whisky, 53 drink beer and brnady, 79 drink beer and whisky, 66 drink brandy and whisky. 21 of them
drink beer, brandy, and whisky. How many are in a group?
a. 302 c. 304
b. 303 d. 405
40. Determine x so that 2x+ 1, 10x-15, 2 x 2+ 9 will be in arithmetic progression.
a. 5 c. 7
b. 6 d. 8
41. A man owns pigs in his barn. He had purchased feed that will last for 75 days for his livestock. The pigs were then infested
with disease. If the man has 4,950 pigs initially and 25 pigs die each day for how long will the feed last?
a. 85 days c. 125 days
b. 100 days d. 297 days
42. In a family, the three children’s ages are in geometric progression. When the youngest child ws born, the oldest was thrice
as old as the second child. In 3 years, the sum of the ages of the second and the youngest child will be equal to the age of
the oldest. How old was the oldest child when the youngest child was born?
a. 3 years old c. 12 years old
b. 27 years old d. 9 years old
43. The side of a square is 36 cm. a second square is formed by joining, in the proper order the third points of the sided of the
first square. A third square is formed by joining the third points of the second square, as so on, find the side of the 25 th
square.
a. 0.0129 cm b. 0.0232 cm
 c. 0.0173 cm d. 0.0331 cm
44. Find the limiting value of 0.38444…
a. 317/450 c. 173/450
b. 371/450 d. 137/450
45. The sum of an infinite geometric series is 8. Each item in the series is 4 times the sum of all the terms that follows it. Find
the fourth term.
a. 8/625 c. 32/625
b. 16/625 d. 64/625
46. Three numbers are in harmonic progression. If the third number were decreased by 4 they would be in arithmetic
progression. If the third number were decreased by 3 they would be arithmetic progression. Find the third term of the
harmonic progression.
a. 0 c. 16
b. 18 d. 12
47. Find the nth term for the sequence 1/3, 2/5,3/7,4/9,…
a. n/(2n+1) c. n/(2n-1)
b. n/(n+1) d. n/(n-1)
x
48. Solve x for the given x x =3
a. 1.224 c. 1.244
b. 1.442 d. 1.242
3 2 n m 12
49. Find the middle term in the expression of (( a + 2b ) is Ca b . Find m.
a. 19 c. 17
b. 20 d. 18
50. The sum of the digits of a three-digit number is 17. If the digits are reserved and the resulting number is added to the
original number, the result is 1,474, if the resulting number is subtracted from the original number, the result is 396. Find
the original number.
a. 935 c. 854
b. 845 d. 953