Military

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1. Which one below has the highest value?

A. 5 × 77 - 25

B. 1200 - 14 × 5

C. 7200 ÷ 12 × 2

D. 900 + 74 × 2

Answer: C

Solution

using BEDMAS

A. 15 × 77 - 55

= 1155 - 55

= 1100

B. 1200 - 14 * 5

= 1200 - 70

= 1130

C. 7200 ÷ 12 × 2

= 600 × 2

= 1200 (highest)

D. 900 + 74 × 2

= 900 + 148

= 1048

2. What is the value of x?

21 - x + 17 + 3x = 4x

a. 38

b. 76

c. 17

d. 19 --- answer

Solution

21 - x + 17 + 3x = 4x

38 + 2x = 4x

38 = 4x - 2x

38 = 2x

x = 38/2

x = 19

checking:

substitute x = 19

21 - x + 17 + 3x = 4x

21 - 19 + 17 + 3(19) = 4(19)

2 + 17 + 57 = 76

19 + 57 = 76

76 = 76

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Friday, August 25, 2023

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

------------

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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Friday, August 18, 2023

CFAT Practice Test Questions with Answers in PROBLEM SOLVING - ps022

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1. Seven years from now, Philip will be ten years younger than two times his current age. What will be his age four years from now?

a. 17

b. 34

c. 21 --- answer

d. 24

Solution

step1

Solve for Philip's current age

Let:

= Philip current age

x + 7

= Philip's age seven years from now

= two times his current age

2x - 10

= ten years younger than two times his current age

Equation:

x + 7 = 2x − 10

7 + 10 = 2x - x

17 = x

x = 17

(Philip's current age)

step2

Solve for Philip's age four years from now

= 17 + 4

= 21

2. Three years ago, Jade was 14 years younger than twice her age now. How old is she seven years from now?

a. 11

b. 18 --- answer

c. 14

d. 22

Solution

step1

Solve for Jade's current age

Let:

= Jade's age now

x - 3

= Jade's age three years ago

= twice her age now

2x - 14

= 14 years younger than twice her age now

Equation:

x - 3 = 2x − 14

14 - 3 = 2x - x

11 = x

x = 11

(Jade's age now)

step2

Solve for Jade's age seven years from now

= 11 + 7

= 18

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Sunday, August 13, 2023

CFAT Practice Test Questions with Answers in PROBLEM SOLVING - ps021

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1. Determine the value of the following:

1 + 74 - 2^2 + 6 x 5

a. 385

b. 101 --- answer

c. 25

d. 100

Solution

using BEDMAS

exponent

multiply

add/subtract L-R

1 + 74 - 2^2 + 6 x 5

= 1 + 74 - 4 + 6 x 5

= 1 + 74 - 4 + 30

= 75 - 4 + 30

= 71 + 30

= 101

2. Calculate the value of:

84 ÷ (4×3) - (4+3) - 1

a. -1 --- answer

b. 15.8

c. 16.8

d. 1

Solution

using BEDMAS

brackets

division

subtraction

84 ÷ (4×3) - (4+3) - 1

= 84 ÷ 12 - 7 - 1

= 7 - 7 - 1

= 0 - 1

= -1

3. Solve the following:

62 × 6^2 - 2^3 ÷ 6^0

a. 1736

b. 2422

c. 4222

d. 2224 --- answer

Solution

using BEDMAS

exponents

multiply

divide

subtract

62 × 6^2 - 2^3 ÷ 6^0

= 62 × 36 - 8 ÷ 1

= 2232 - 8

= 2224

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Friday, August 11, 2023

CFAT Practice Test Questions with Answers in PROBLEM SOLVING - ps020

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1. In Alberta, the average cost to paint an interior room in a house is $2.10 per square foot. A house has the following rooms for painting:

Bedroom A: 689 sqft

Bedroom B: 746 sqft

Bedroom C: 828 sqft

Living Rm: 1727 sqft

Kitchen: 585 sqft

BathroomA: 412 sqft

BathroomB: 381 sqft

Laundry: 274 sqft

What is the total cost of painting before taxes?

a. $10,884

b. $11,488

c. $11,848 -- answer

d. $12,844

Solution

step1

find total sqft

= 689 + 746 + 828 +

1727 + 585 + 412 +

381 + 274

= 5,642 sqft

step2

multiply total sqft by cost per sqft

Total Painting Cost

= 5,642 sqft

x $2.10/sqft

= $11,848

2. The average cost to fence a yard in Canada is $55 per linear ft. If the total fencing cost of a square yard is $9,240, find the length of one side.

a. 40 ft

b. 42 ft --- answer

c. 41 ft

d. 43 ft

Solution

step1

divide total cost by cost per linear foot

Total linear feet

= 9,240/55

= 168 ft

step2

divide total linear feet by 4 to get one side of the square yard

side of square yard

= 168/4

= 42 ft

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Saturday, August 5, 2023

CFAT Practice Test Questions with Answers in PROBLEM SOLVING - ps019

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1. An investor's portfolio increased by 43.9% to $210,000. What was his initial investment?

a. $143,595

b. $145,935 --- Ans

c. $154,395

d. $149,435

Solution

Given

43.9% increase

$210,000 new value

let

x = initial investment

210,000

= x + 43.9% x

= x + 0.439x

= 1.439x

x = 210,000/1.439

x = $145,935

2. The price of gold per ounce (oz) is $1,944.10 USD. With an investment of $49,000 USD, how many ounces of gold can you purchase?

a. 23.5 oz

b. 24.2 oz

c. 22.5 oz

d. 25.2 oz --- answer

Solution

Divide the amount of investment by the price of gold per ounce.

ounces (oz) of gold

= 49,000/1,944.10

= 25.2 oz

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Wednesday, August 2, 2023

CFAT Practice Test Questions with Answers in PROBLEM SOLVING - ps018

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1. One week is equivalent to 604,800 seconds. If an average person sleeps 7 hours a day, what percent does an average person sleeps in a week?

a. 33%

b. 32%

c. 29% --- answer

d. 30%

Solution

step1

convert 7 hours to seconds

daily sleep sec

= 7 hr x 3600 sec/hr

= 25,200 sec/day

step2

calculate weekly sleep in seconds

weekly sleep sec

= 25,200 sec x 7 day

= 176,400 sec/week

step3

calculate percent sleep

= 176,400/604,800

= 29%

2. The population of Canada on May 2023 is 39,860,000. If 23% of Canadians speak French, what number does this represent?

a. 9,178,800

b. 9,176,800

c. 9,168,800

d. 9,167,800 --- Ans

Solution

Using long multiplication,

= 39,860,000 x 23%

= 39,860,000 x 0.23

= 9,167,800

3. Which number is missing in the following sequence?

1/16, 1/4, 7/16, ____

a. 11/16

b. 5/8 ---- answer

c. 3/8

d. 2/4

Solution

The sequence is increasing by 3/16

1/16

1/16 + 3/16

= 4/16

= 1/4

4/16 + 3/16

= 7/16

7/16 + 3/16

= 10/16

= 5/8

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