CFAT Practice Test Questions with Answers in PROBLEM SOLVING - ps023

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1. One half of a certain number is 5 more than 3/7 of the number. Find the number. 

a. 35

b. 70  --- answer 

c. 14

d. 5

Solution 

Let x 

= unknown number

formulate equation 

(1/2)x = 5 + (3/7)x 

(1/2)x - (3/7)x = 5 

factoring 

x (1/2 - 3/7) = 5

LCD

x ( 7 - 6 )  = 5

   ------------ 

       14

x (1/14) = 5 

x = 14 * 5

x = 70

checking 

(1/2)x = 5 + (3/7)x 

(1/2)70 =5 + (3/7)70

35 = 5 + 3(10)

35 = 5 + 30

35 = 35

2. Five loaves of bread and ten bananas have a total cost of $22.75. One loaf of bread and one banana have a total cost of $4.15. How much does a loaf of bread cost and how much does one banana cost?

a. $3.25, $0.25

b. $3.50, $0.30

c. $2.75, $0.35

d. $3.75, $0.40   --- answer 

Solution 

Let 

x = cost of one loaf of bread 

y = cost of one banana

equation1

5x + 10y = 22.75

equation2

x + y = 4.15

x = 4.15 - y

substitute the value of x in equation2 into equation1

5x + 10y = 22.75

5 (4.15 - y) + 10y = 22.75 

20.75 - 5y + 10y = 22.75

20.75 + 5y = 22.75

5y = 22.75 - 20.75

5y = 2

y = 2/5

y = $0.40 

(cost of one banana)

solve for x:

substitute the value of y into equation2

x = 4.15 - y

x = 4.15 - 0.40

x = $3.75

(cost of one loaf of bread)

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