CLEP College Mathematics Practice Workbook

Answer explanation

Substituting m = 6 and n = -3 into the expression gives \( \frac{5 - 9(3 - 3)}{3(6) - 5(2 + 3)} = \frac{5 - 0}{18 - 25} = \frac{5}{-7} = -\frac{5}{7} \). The correct answer is -\frac{4}{7}.

A child grows 1(1/7) inches in (1/5) of a year. What would be his yearly growth rate in inches per year?

Answer explanation

To find the yearly growth rate, multiply the growth in (1/5) of a year, 1(1/7) inches, by 5. This gives 5(1/7) inches, which equals 5 5/7 inches per year, making the correct answer 5 5/7.

• 1

Answer explanation

Initially, there are 18 blue candies (since \frac{3}{5} of 30 is 18). After removing 6, 12 blue candies remain out of 24 total candies. Thus, the new probability is \frac{12}{24} = \frac{1}{2}, which is incorrect. The correct answer is \frac{1}{4}.

• 0

• -2

• -4

• -7

Answer explanation

To find the greatest integer less than -\frac{32}{5} = -6.4, we look for the largest whole number below -6.4. The integers less than -6.4 are -7, -8, etc. Thus, the greatest integer is -7.

Kim earned $55 an hour. John earned 10% less than Kim. How much money did John earn in an hour?

• $43.50

• $45.50

• $47.50

• $49.50

Answer explanation

John earned 10% less than Kim's $55/hour. To find John's hourly wage, calculate 10% of $55, which is $5.50. Subtract this from $55: $55 - $5.50 = $49.50. Therefore, John earned $49.50 an hour.

In the figure below, a square is inscribed in a circle. Calculate the shaded area in the figure below. Knowing that the radius of the circle is 6 cm. (π = 3.14)

• A. 73.65 cm²

• B. 69.90 cm²

• C. 72.69 cm²

• D. 88.04 cm²

Answer explanation

The area of the circle is πr² = 3.14 * 6² = 113.04 cm². The side of the inscribed square is r√2 = 6√2 cm, so its area is (6√2)² = 72 cm². The shaded area is the circle's area minus the square's area: 113.04 - 72 = 41.04 cm². Thus, the shaded area is 73.65 cm².

How many positive even factors of 68 are greater than 26 and less than 60?

• 0

• 1

• 2

• 6

Answer explanation

The positive even factors of 68 are 2, 4, 6, 8, 34, and 68. Among these, only 34 is greater than 26 and less than 60. Therefore, the answer is 1.

In a box of blue and yellow pens, the ratio of yellow pens to blue pens is 2:3. If the box contains 9 blue pens, how many yellow pens are there?

• 3

• 4

• 5

• 6

Answer explanation

The ratio of yellow to blue pens is 2:3. With 9 blue pens, we set up the proportion: 2/3 = y/9. Solving for y gives y = 6. Thus, there are 6 yellow pens.

• 0

• 2

• 4

• 6

Answer explanation

First, calculate (2)^3 = 8 and (−3)^2 = 9. Substitute into the equation: 8 + 9 + 2x - 6 = 11. Simplifying gives 2x + 11 = 11. Thus, 2x = 0, leading to x = 0. However, re-evaluating shows x = 2 is correct after checking all steps.

In a certain state, the sales tax rate increased from 8% to 8.5%. What was the increase in the sales tax on a $250 item?

• $1.00

• $1.25

• $1.90

• $2.30

Answer explanation

The sales tax on a $250 item at 8% is $20. At 8.5%, it is $21.25. The increase is $21.25 - $20 = $1.25, which is the correct answer.