1. What number is as much more than 8 as it is less than 32 ?

a. 20

b. 40

c. 60

d. cannot be determined from the given information

____________2. A container van that is 3 meters wide, 5 meters long and 4 meters
high will transport 200 crates whose volume is 6 cubic meters. How many trips will
it take to transport all the crates?

a. 20

b. 25

c. 30

d. 35

____________3. A rectangular block of copper, with dimensions 4m x 6m x 9m, is

melted and recast into a cubical block. Find the length of the side of the cubical
block.

a. 4 cm

b. 6 cm

c. 9 cm

d. 12 cm

____________4. There are 9 male teachers for every 14 female teachers. If there are
69 teachers in all, how many teachers are female?

a. 18

b. 27

c. 39

d. 42

___

____________5. What would be the closest approximation to 66 ?

a. 7.9
 b. 8

c. 8.1

d. 8.9

__________6. Manny can do a certain job in 1 day, Anna can do the same job in 2
days, and Josie can do the job in 3 days. How many days will it take them to do the
job if they work together?

a. 1/6

b. 1/3

c. 6/11

d. 1/2

__________7. In the figure, all the line segments meet at right angles and each
segments has a length of 1 unit. What is the area of the figure in square units?

a. 9

b. 12

c. 16

d. 25
___________8. If x - 3 = y, then (y - x )3 = _____ ?

a. 9

b. -27

c. 27

d. 81

___________9. A speed of 90 km per hour is equivalent to how many meters per

second?

a. 20

b. 25

c. 30

d. 45

___________10. A rectangular sheet of cardboard 5 inches long and 4 inches wide is

cut into squares one inch on a side. What is the maximum number of such squares
that can be formed?

a. 18

b. 20

c. 9

d. 16

11. A housewife bought 3 kilograms of beef priced at $ 108.75 per kilogram. How
much change did she receive from a five-hundred dollar bill?

a. $ 163.25

b. $ 193.75

c. $ 173.75

d. $ 180.25

___________12. A delivery of 480 baskets of mangoes is divided into two fruit stands
so that the difference between the two orders is 1/3 their average. What is the ratio
of the smaller to the larger amount?

a. 5 : 7
 b. 5 : 9

c. 5 : 12

d. 2 : 3

___________13. When the first and the last digits of 2, 836 are interchanged, the new
number is _____.

a. 3996 more than 2, 836

b. 3996 less than 2, 836

c. 1404 more than 2, 836

d. 1404 less than 2, 836

___________14. If twice the value of a certain number is increased by 8 the result is

40. What is the number?

a. 8

b. 16

c. 24

d. 32

___________15. In a group of 120 persons, there are 32 more women than men. How
many women are there in the group?

a. 44

b. 76

c. 88

d. 92

_16. If the dimensions of a square change in such a manner that the area remains
constant, what must happen to the other side if one side will be increased by 1/4 of
itself?

a. it decreases by 1/5

b. it decreases by 1/4

c. it decreases by 1/3

d. it decreases by 1/2
___________17. A man rowed 4 miles upstream for 2 hours. If the river flowed with a
current of 2 miles per hour, how long did the man's return trip take?

a. 1/3 hour

b. 1/2 hour

c. 2/3 hour

d. 1 hour

___________18. The rectangle shown in the figure is divided into 6 equal squares. If
the perimeter of the rectangle is 42 cm, what is the area of each square in cm 2 ?

a. 6

b. 9

c. 12

d. 15

__________19. If the area of the rectangle ABCD shown below is 36 units, how many
square units is the area of the shaded region?
 a. 12

b. 16

c. 18

d. 24

___________20. This tank holds 48 liters of gasoline and the car averages 5
kilometers per liter. Approximately how many kilometers can a car travel this given
guage?

a. 12

b. 24

c. 30

d. 60

___________21. Which of the following graphs represents the taxi rates for a company
that charges $ 3.50 for the first 200 meters and $ 1.00 for each additional 100
meters?

a.
b.
c.
d.
____________22. A laboratory assistant was preparing a solution that should have
included 40 milligrams of chemical. If he actually used 41.30 milligrams, what was
his percentage error (to the nearest 0.01 %)?

a. 0.0325%

b. 0.325%

c. 3.25%

d. 32.5%
_23. Menthol drops come in packs of 8 for $ 3.60. Butterballs come in packs of 6 for
$ 2.25. Aidabought 48 pieces of candy. How many of each kind of candy did she
buy, if she spent $ 19.80?

a. 6 packs of Menthol drops and no Butterballs

b. 3 packs of Menthol drops and 4 packs of Butterballs

c. 8 packs of Butterballs and no Menthol drops

d. Choices A, B, and C are possibilities

Use the following table for questions 24 and 25.

___________24. How much tax is due on a taxable income of $65, 000?

a. $ 6, 075

b. $ 6, 050

c. $ 6, 094

d. $ 7, 025
___________25. How much tax is due on a taxable income of $55, 000?

a. $ 4, 575

b. $ 5, 325

c. $ 6, 825

d. $ 18, 075

______26. Anabelle paid $ 19, 675 tax. If x was her income, which of the
following statements is TRUE?

a. $ 60, 000 < x < $ 100, 000

b. $ 100, 000 < x < $ 250, 000

c. $ 40, 000 < x < $ 60, 000

d. $ 250, 000 < x < $ 500, 000

__________27. Mang Pablo decided to keep a record of the money he collects from his
newspaper route. Using the information given, how much money does Mang Pablo
collect in the month of February? (Note : Assume that February has 28 days and the
February 1 was on a Sunday).

NUMBER
WEEKLY OF
DELIVERY INCOME
RATE CUSTOMER
S

Daily Except Sunday $ 42 x 75 $ 3, 150

Sunday Only $ 10 x 60 $ 600

all week
$ 52 x 120 $ 6, 240
(daily and Sunday)

a. $ 9, 990

b. $ 19, 980

c. $ 39, 960

d. $ 49, 950
__________28. If 10 soldiers can survive for 12 days in 15 packs of rations, how
many packs will be needed for 8 men to survive for 18 days?

a. 16 packs

b. 17 packs

c. 18 packs

d. 19 packs

___________29. If it takes Victor twice as long to earn $ 600 as it takes Warnen to

earn $ 400, what is the ratio of Victor's per day to Warnen's pay per day?

a. 3 : 1

b. 3 : 2

c. 3 : 4

d. 4 : 3

See the following table for the question 30 to 32.

TYPE OF VEHICLE - COST OF FUEL FOR 100 - KM TRIP

Car - $ 500 truck - $ 2, 000

motorcycle - $ 175 airplane - $ 3, 000

Bus - $ 875

__________30. What is the cost of fuel for a 120-km trip by car?

a. $ 400

b. $ 480

c. $ 520

d. $ 600
__________31. If the total wages of a bus driver for 100-km trip is $ 970, and the only
cost for a bus are the fuel and the driver's wage. How much should a bus
company charge to charter a bus with a driver for a 200-km trip in order to obtain
50% more than the cost?

a. $ 2, 330

b. $ 5, 535

c. $ 2, 720

d. $ 2, 767.50

__________32. If 5 buses, 9 cars, 4 motorcycles make a 100-km trip. What is the

average fuel cost per vehicle?

a. $ 521.94

b. $ 526.67

c. $ 531.94

d. $ 516.67

__________33. A store owner bought 2 dozen cans of corned beef at $ 30 each. He

sold two-thirds of them at 25% profit but was forced to take a 30% loss on the rest.
What was his total profit (or loss) on the item?

a. a loss of $ 48

b. a gain of $ 48

c. no gain or loss

d. gain of $ 4

e the table below for questions number 34 to 36.

% OF % OF
% OF COST PER
PROTEI CARBOHYDRAT
VITAMINS 100 GRAM
N ES

Salad A 20 15 40 $ 25.00

Salad B 10 25 30 $ 30.00

Salad C 20 10 50 $ 35.00
___________34. The cost of x purchasing grams of Salad A, y grams of Salad B and z
grams if Salad C will be ________.

a. (25x + 30y + 35z) pesos

b. 90 xyz pesos

c. (25x + 30y + 35z) cents

d. (5x + 6y + 7z) dollars

___________35. Which of the following diets would supply the most grams
of vitamins?

a. 500 grams of Salad A

b. 400 grams of Salad B

c. 200 grams of Salad A, 100 grams of Salad B and 200 grams of Salad C

d. 200 grams of Salad A, 50 grams of Salad B and 200 grams of Salad C

___________36. All of the following diets would supply at least 85 grams of

carbohydrates. Which of the dietscosts the least?

a. 100 grams of Salad A, 200 grams of Salad B and 300 grams of Salad C.

b. 300 grams of Salad A, 100 grams of Salad B and 200 grams of Salad C.

c. 200 grams of Salad A, 100 grams of Salad B and 300 grams of Salad C.

d. 100 grams of Salad A, 300 grams of Salad B and 200 grams of Salad C.

37. If jackfruits are twice as expensive as watermelons, and watermelons are one-
third as expensive as durians. What is the ratio of the price of one jackfruit to one
durian?

a. 3 : 2

b. 2 : 3

c. 6 : 1

d. 1 : 6
_________38. A retailer buys a pack of sugar from Uniwide Sales for $459. He then
marks up the price by 1/3 and sells it at a discount of 16 and 2/3 %. What was his
profit in this item?

a. $ 153

b. $ 102

c. $ 26.50

d. $ 51.00

_________39. Forrest Gamp walks down the road for 30 minutes at a rate of 3 mph.
He waits 10 minutes for a bus, which brings him back to his starting point at 4 : 25.
If he began his walk at 3:35 the same afternoon, what was the average speed on
the bus?

a. 3 mph

b. 4.5 mph

c. 7.5 mph

d. 9 mph

_________40. Miss Felisa Gascon had $ 2 million to invest. She invested part of it at
4% a year and theremainder at 5% per year. After one year she earned $ 95, 000 in
interest. How much of the originalinvestment was placed at 5% rate?

a. $ 900,000

b. $ 1,250,000

c. $ 1,500,000

d. $ 1,600,000

a.
0

b. 1

c. 3

d. 5

________42. In a building plan, 1/4 cm represents 2 meters. If the main entrance is

supposed to be 8 meters wide, how would its representation be on the plan?

a. 1 cm
 b. 1/2

c. 2 cm

d. 1/16 cm

________43. A real estate agent marks a certain property up 40% above the
original cost. Then he gives aclient a 15% discount. If the final selling price of the
property was $8.619 M, what was the original cost of the property?

a. $ 6.63 M

b. $ 7.26 M

c. $ 7.8 M

d. $ 99.12 M

________44. If 2/3 the perimeter of a square is 16, then what is the length of one of
its sides?

a. 6

b. 8

c. 9

d. 12

________45. What values of x can satisfy the equation (3x + 6) (2x - 8) = 0?

a. -4 and 2 only

b. 4 only

c. -2 only

d. -2 and 4 only

_46. If 8 men can plant 288 trees in one day, how many trees can 12 men plant in 5
days?

a. 432

b. 960

c. 1,800

d. 2,160
________47. If the length of a rectangle is increased by 25% and its width is
decreased by 20%, what happens to the area of the rectangle?

a. increase by 5%

b. decrease by 5%

c. increase by 45%

d. no change

________48. The formula for the volume of a sphere is V = 4/3 3. If the radius (r) is
tripled, what will be the ratio of the new volume to the original volume?

a. 1 : 3

b. 3 : 1

c. 9 : 1

d. 27 : 1

________49. The scale on a map is 1 : 8. If a surveyor reads a certain measurement

on the map as 4.6 cm instead of 5.0 cm, what will be the resulting approximate
percent error on the full size model?

a. 4%

b. 8%

c. 64%

d. 93%

________50. In a certain recipe, 225 grams of beef are called for to make 6 servings.
If Mrs. Alferez wants to use the recipe for 8 servings, how many grams of beef must
she use?

a. 275 grams

b. 300 grams

c. 337.5 grams

d. 400 grams

Mathematics Test 5
1. A

2. A

3. B

4. D

5. C

6. C

7. D

8. B

9. B

10. B 11. C

12. A

13. A

14. B

15. B

16. A

17. C

18. B

19. C

20. D 21. B

22. C

23. B

24. D

25. B

26. B

27. A

28. C
29. D

30. D 31. B

32. C

33. B

34. C

35. C

36. B

37. B

38. D

39. D

40. C 41. D

42. A

43. C

44. A

45. B

46. D

47. D

48. D

49. B

50. B

Solutions

1. What number is as much more than 8 as it is less than 32 ?

Let x - be the number

x - 8 = 32 - x
x + x = 32 +8
 2x = 40
x = 40 / 2
x = 20 * Ans.

2. A container van that is 3 meters wide, 5 meters long and 4 meters high will
transport 200 crates whose volume is 6 cubic meters. How many trips will it take to
transport all the crates?

Let N - be the number of trips

No. of trips = (No. of crates) x volume x 1 trip

crate volume of the van

N = 200 crates x 6 m3 x 1 trip

crate (3 x 5 x 4)m3

N = (200) (6)
3x4x5

N = 1200
60
N = 20 trips * Ans.

3. A rectangular block of copper, with dimensions 4m x 6m x 9m, is melted

and recast into a cubical block. Find the length of the side of the cubical block.

Vcubical block = Vrectangular block

S3 = (4 x 6 x 9) m3

S3 = 216 m3
______
S = 216 m3

S = 6m * Ans.

4. There are 9 male teachers for every 14 female teachers. If there are
69 teachers in all, how many teachersare female?

9 : 14 = Male : Female
 23 69

No. of Female teachers = (69 / 23) x 14

= 3 x 14
= 42 * Ans.

___
5. What would be the closest approximation to 66 ?
___
64 = 8
___
66 8.1 * Ans.

One 1 day Manny can finish the whole job

Anna can finish 1/2 of the same job
Josie can finish 1/3 of the same job

Let N - be the days that it takes to finish the job if they work together.

(1 + 1 + 1)N=1
1 2 3

(6 + 3 + 2)N=1
6

11 N = 1
6
N = 1 x 6 (reciprocal of 11 / 6)
11
N = 6 / 11 day * Ans.

7. In the figure, all the line segments meet at right angles and each
segments has a length of 1 unit. What is the area of the figure in square
units?
8. If x - 3 = y, then (y - x )3 = _____ ?

If x - 3 = y;

-3 = y - x
(-3)3 = (y - x)3
-27 = (y - 3)3 * Ans.

9. A speed of 90 km per hour is equivalent to how many meters per

second?

= 90 km x 1 hr x 1000 m
hr 3600 sec km

= 90 x 1000 m
3600 hr

= 25 m * Ans.
sec

10. A rectangular sheet of cardboard 5 inches long and 4 inches wide is

cut into squares one inch on a side. What is the maximum number of such
squares that can be formed?

There are 20 squares * Ans

11. A housewife bought 3 kilograms of beef priced at $ 108.75 per

kilogram. How much change did she receive from a five-hundred dollar
bill?

Change = $ 500 - (3 x $ 108.75)

= $ 500 - $ 326.25
= $ 173.75 * Ans.

12. A delivery of 480 baskets of mangoes is divided into two

fruit stands so that the difference between the two orders is 1/3 their
average. What is the ratio of the smaller to the larger amount?

Let x - be the no. of baskets in the fruit stand.

Let 480 - x be the number in the second fruit stand.

(480 - x) - x = 1 (x + y) ------> 480 - 2x = 80

3 2 ------> 2x = 480 - 80
------> 2x = 400
but x + y = 480 1 ( 480 ) ------> x = 200 480 - x
= 280
since the total 3 2
delivery = 480
The ratio is 200 : 280 = 5 : 7 * Ans.
40 40

13. When the first and the last digits of 2, 836 are interchanged, the new
number is ________.

6,832 -----> the new number

6,832 - 2836 = 3996

therefore, the new number is 3,996 more than 2,836 * Ans.

14. If twice the value of a certain number is increased by 8 the result is

40. What is the number?

Let x - be the number

2x + 8 = 40
2x = 40 -8
2x = 32
x = 32 / 2
x = 16 * Ans

15. In a group of 120 persons, there are 32 more women than men. How
many women are there in the group?

Let x - be the number of women

Let x - 32 be the number of men

x + ( x - 32 ) = 120
2x - 32 = 120
2x = 120 + 32
2x = 152
x = 152 / 2
x = 76 women * Ans.

16. If the dimensions of a square change in such a manner that the area
remains constant, what must happen to the other side if one side will be
increased by 1/4 of itself?

(s + 1 s) y = s (s)
4

5 ( s )( y )= s2
4

y = s2 ( 4 )
5s
y= 4 s
5
s=- 4 s = 1 s
5 5

therefore, it decreased by 1/5 of itself * Ans.

17. A man rowed 4 miles upstream for 2 hours. If the river flowed with a
current of 2 miles per hour, how long did the man's return trip take?

Let x - be the rate of the boat in still water

Let 2x - be the rate of the boat upstream
Let 2 mph - be the rate of the current
Let (x + 2) - speed of the boat downstream

rateup x time = distance

(x - 2) (2) = 4
2x - 4 = 4
2x = 4 + 4
 2x = 8
x = 4 miles / hr

ratedown x time = distance

(x+2) (time) = 4
(4+2) (time) = 4
6 (time) = 4
time = 4 / 6
time = 2 / 3 hrs. * Ans.

18. The rectangle shown in the figure is divided into 6 equal squares. If
the perimeter of the rectangle is 42 cm, what is the area of each square in
cm2 ?

14x = 42

x = 42 / 14

x = 3 cm.

Area of the squares = x2

= (3 cm)2

= 9 cm2 * Ans.
19. If the area of the rectangle ABCD shown below is 36 square units, how
many square units is the area of the shaded region?

Arectangle = bh
Arectangle = 36
bh = 36

Atriangle = 1/2 bh
= 1/2 (36)
= 18 sq. units * Ans.

20. This tank holds 48 liters of gasoline and the car averages 5 kilometers
per liter. Approximately how many kilometers can a car travel this given
guage?

The guage indicates that the tank is 1/4 full.

Let N - be the number of kilometers that can be traveled.

N = ( 1 tank) x 48 liters x 5 km

4 tank liter

= 1/4 x 48 x 5 km
= 60 km. * Ans

21. Which of the following graphs represents the taxi rates for a company
that charges $ 3.50 for the first 200 meters and $ 1.00 for each additional
100 meters?

This is the approximate graph for the taxi rate, there is an abrupt change
in the fare for every 100 meters change in the distance.

* Ans.

22. A laboratory assistant was preparing a solution that should have

included 40 milligrams of chemical. If he actually used 41.30 milligrams,
what was his percentage error (to the nearest 0.01 %)?

% error = error x 100%

correct value
 = 41.30 - 40 x 100%
40
= 1.3 %
40
= 130 %
40
= 3.25 % * Ans

23. Menthol drops come in packs of 8 for $ 3.60. Butterballs come in packs of 6 for $
2.25. Aida bought 48 pieces of candy. How many of each kind of candy did she buy,
if she spent $ 19.80?

b. 3 packs of Menthol drops and 4 packs of Butterballs.

= (3 x $ 3.60) + (4 x $2.25)
= $ 10.80 + $ 9.00
= $ 19.80 * Ans.

Use the following table for questions 23 and 24.

24. How much tax is due on a taxable income of $65, 000?

Tax due = $6, 075 + 0.19 ($65,000 - $60,000)
= $6, 075 + 0.19 ($5,000)
= $6, 075 + $950
Tax due = $7, 025 * Ans.

25. How much tax is due on a taxable income of $55, 000?

Tax due = $3, 075 + 0.15 ($55,000 - $40,000)

= $3, 075 + 0.15 ($15,000)
= $3, 075 + $2,250
Tax due = $5, 325 * Ans.

26. Anabelle paid $ 19, 675 tax. If x was her income, which of the following
statements is TRUE?

b. $ 19, 675 tax due belongs to this range * Ans.

Over $ 100, 000 but not over $ 250, 000

$ 13, 675 + 24% of excess over $ 100, 000

therefore, Anabelle's income is between $ 100,000 and $ 250,000

27. Mang Pablo decided to keep a record of the money he collects from his
newspaper route. Using the information given, how much money does
Mang Pablo collect in the month of February? (Note : Assume that
February has 28 days and the February 1 was on a Sunday).

WEEKLY NUMBER OF
DELIVERY INCOME
RATE CUSTOMERS

Daily Except Sunday $ 42 x 75 $ 3, 150

Sunday Only $ 10 x 60 $ 600

all week
$ 52 x 120 $ 6, 240
(daily and Sunday)
* Ans - Total $ 9, 990

28. If 10 soldiers can survive for 12 days in 15 packs of rations, how many
packs will be needed for 8 men tosurvive for 18 days?

Let N - be the number of packs

N packs -----> 15 packs ---> N = 15 x (8 x 18) packs

8 men x 18 days 10 men x 12 days 10 x 12

N = 18 packs * Ans.

29. If it takes Victor twice as long to earn $ 600 as it takes Warnen to earn
$ 400, what is the ratio of Victor's per day to Warnen's pay per day?

Warnen earns 400 in x days

Victor earns 600 in 2x days
Therefore he earns 300 in 2x days

The ratio of Victor's pay to

Warnen's pay in x days is 400 : 300 or 4 : 3 * Ans

Use the following table for questions no. 30 - 32.

TYPE OF VEHICLE - COST OF FUEL FOR 100 - KM TRIP

car - $ 500 motorcycle - $ 175

bus - $ 875 truck - $ 2,000

airplane - $ 3, 000

30. What is the cost of fuel for a 120-km trip by car?

Cost of fuel = 120 km x $ 500 ----> 120 x $ 5 -----> $ 600 *Ans.

 100 km

31. If the total wages of a bus driver for 100-km trip is $ 970, and the only
cost for a bus are the fuel and the driver's wage. How much should a bus
company charge to charter a bus with a driver for a 200-km trip in order
to obtain 50% more than the cost?

Cost for a 100-km trip = Cfuel + Cdrives ------> 875 + 970 ------> $
1,845

Total Cost = ( $ 1, 845 x 200 km ) x 1.50 ------> $ 5, 535 * Ans.

100 km

32. If 5 buses, 9 cars, 4 motorcycles make a 100-km trip. What is the

average fuel cost per vehicle?

Average Cost = total cost of fuel ----> (5 x $ 875) + (9 x $ 500) + (4 x $

175)
total no. of vehicle 5+9+4

$ 4375 + $ 4500 + $ 700 ------> $ 9575 ----> $ 531.94 * Ans

5+9+4 18

33. A store owner bought 2 dozen cans of corned beef at $ 30 each. He

sold two-thirds of them at 25% profit but was forced to take a 30% loss on
the rest. What was his total profit (or loss) on the item?

Total Selling Price

= [ 2 (24 cars) x $ 30 x ( 1 + 0.25 )] + [ 1 (24 cars x $ 30 ) ( 1 - 0.30 )]

3 car 3 car

= [ 2 (24) x $ 30( 1.25 )] + [ 1 (24)($ 30)(0.70)]

3 3

Total Selling Price = $ 600 + $ 168

= $ 768
Total cost = $30 x 24 cars = $720
car

Gain = Total selling price - Total cost

= $ 768 - $ 720
= $ 48 * Ans.

Use the table below for questions no. 34 - 36.

% OF % OF
% OF COST PER
PROTEI CARBOHYDRA
VITAMINS 100 GRAM
N TES

Salad
20 15 40 $ 25.00
A

Salad
10 25 30 $ 30.00
B

Salad
20 10 50 $ 35.00
C

34. The cost of x purchasing grams of Salad A, y grams of Salad B and z

grams of Salad C will be _____.

Cost of Salad A = $ 200 x x gm x 100 =

25x
100 gm P 1,000

Cost of Salad B = $ 30 x y gm x 100 =

30y
100 gm P 1,000

Cost of Salad C = $ 35 x z gm x 100 =

35z
 100 gm P 1,000

therefore, the total cost is (25x + 30y + 35z) cents * Ans.

35. Which of the following diets would supply the most grams of vitamins?

c. Salad A + 50g Salad B + (300 g) Salad C

= 0.40 (200) + 0.30 (100) + 0.50 (200) ----> 80 + 30 + 100 ----> 210 gms *
Ans.

36. All of the following diets would supply at least 85 grams of

carbohydrates. Which of the diets costs the least?

b. $ 25 (3) + $ 30 (1) + $ 35 (2)

$ 75 + $ 30 + $ 70 = $ 175 * Ans.

37. If jackfruits are twice as expensive as watermelons, and watermelon is

one-third as expensive as durians. What is the ratio of the price of one
jackfruit to one durian?

Let x - be the cost of watermelon

Let 2x - be the cost of the jackfruit
Let 3x - be the cost of the durian

= Jackfruit : Durian
= 2x : 3x
= 2 : 3 * Ans.

38. A retailer buys a pack of sugar from Uniwide Sales for $ 459. He then
marks up the price by 1/3 and sells it at a discount of 16 2/3 %. What was
his profit in this item?

Marked price = $ 459 + 1/3 ($ 459) ----------> 459 + $ 153 -------> $

612
Discounted Price = $ 612 - 16 % ($ 612) ---------> $ 612 - 1/6 ($ 612) ------>
$ 510

Profit = Selling Price - Cost

= $ 510 - $ 459
= $ 51 * Ans.

39. Forrest Gump walks down the road for 30 minutes at a rate of 3 MPH.
He waits 10 minutes for a bus, which brings his back to his starting point
at 4 : 25. If he begun his walk at 3 : 35 the same afternoon, what was the
average speed on the bus?

dwalked = rate x time

= 3 mi. x 1 hr. ------> dwalked = 1.5 miles

hr. 2

timetravelled by the bus = 4:25 - 3:35 - :30 - :10 ------> 10 mins ----> 1/6 hr.

speedof the bus = distance --------> 1.5 minutes ---> (1.5 x 6) mi/hr ---> 9
mi/hr * Ans.
time 1/6 hr

40. Miss Felisa Gascon had $ 2 million to invest. She invested part of it at
4% a year and the remainder at 5% per year. After one year she earned $
95, 000 in interest. How much of the original investment was placed at 5%
rate?

Let x - be the amount of invested at 5%

Let 2,000,000 - x be the amount invested at 4%

0.05x + 0.04 (2,000,000 - x) = 95000

0.05x + 80000 - 0.04x = 95000
0.01x = 95000 - 80000
0.01x = 15000
x = 15000 / 0.01
x = 1, 500, 000 * Ans.
42. In a buidling plan, 1/4 cm represents 2 meters. If the main entrance is
supposed to be 8 meters wide, how wide would its representation be on
the plan?

Let N - be the representation of the plan

1/4 : 2 = N : 8

2N = (1/4) (8)
2N = 8/4
2N = 2
N = 2/2
N = 1 cm. * Ans.

43. A real state agent marks a certain property up 30% above the
original cost. Then he gives a client a 15% discount. If the final selling
price of the property was $8.619 M, what was the original cost of the
property?

Let x - be the original cost

(x + 0.30x) ( 1 - 0.15) = $8.619 M

(1.30x) (0.85) = $8.619 M
1.105x = $8.619 M
x = $8.619 M / 1.105
x = 7.8 M * Ans.

44. If 2/3 the perimeter of a square is 16, then what is the length of one of
its sides?

2/3 P = 16
P = 16 (3/2)
P = 48/2
P = 24

Perimeter formula for SQUARE is P = 4S.

P = 4S
24 = 4S
 24 = 4S
24/4 = S
6=S

therefore, S = 6 * Ans.

45. What values of x can satisfy the equation (3x + 6) (2x - 8) = 0 ?

3x + 6 = 0
3x = -6
x = -6 / 3
x=-2

2x - 8 = 0
2x = 8
x=8/2
x = 4 * Ans.

46. If 8 men can plant 288 trees in one day, how many trees can 12
men plant in 5 days?

Let N - be the number of trees

N= 288 trees x 12 men x 5 days -----> 288 x 12 x 5

8 men - 1 day 8 trees

N = 2, 160 trees * Ans.

47. If the length of a rectangle is increased by 25% and its width is

decreased by 20%, what happens to the area of the triangle?

Aorig. = LW

Anew = L (1+0.25) x W (1 - 0.20)

= L (1.25) x W (0.8) -----> (1.25) (0.8) LW
Anew = 1 x LW
Anew = Aorig.
therefore, no change in the area * Ans.

48. The formula for the volume of a sphere is V = 4/3 r3. If the radius (r)
is tripled, what will be the ratio of the new volume to the original volume?

Vorig. = 4/3 r3

Vnew = 4/3 (3r)3 -----> = 4/3 (27r3) ------> 27 (4/3 r3)

Vnew = 27 Vorig. -----> Vnew : Vorig. = 27 : 1 * Ans.

49. The scale on a map is 1 : 8. If a surveyor reads a certain measurement

on the map as 4.6 cm instead of 5.0 cm, what will be the resulting
approximate percent error on the full size model?

% error = error x 100% -> 5.0 - 4.6 x 100% -> 0.4 x 100% -> 8% *Ans.
correct value 5.0 5

50. In a certain recipe, 225 grams of beef are called for to make 6
servings. If Mrs. Alferez wants to use the recipe for 8 servings, how many
grams of beef must she use?

Let N - be the number of grams required

225 : 6 = N : 8

6N = 8(225)
6N = 1800
N = 1800 / 6
N = 300 grams. * Ans.