# ASVAB Arithmetic Reasoning Test

#### Which of the following is NOT a factor of 90?

A factor must divide evenly into its multiple. 12 cannot be a factor of 90 because 90 divided by 12 = 7.5.

#### How many 1/3 pound paperback books together weigh 25 pounds?

If each book weighs 1/3 pound, then 1 pound = 3 books. We can set up a proportion to solve: 1 pound / 3 books = 25 pounds / x books. Now cross-multiply: (1)(x) = (3)(25) X = 75

#### On a map, the length of the road from Town F to Town G is measured to be 18 inches. On this map, ¼ inch represents an actual distance of 10 miles. What is the actual distance, in miles, from Town F to Town G along this road?

Here we are given a ratio: ¼ inch on the map = 10 miles, so 1 inch on the map = 40 miles. If the map-distance between the towns is 18 inches, then the actual distance must be 18 x 40 = 720.

#### Lisa and Robert have taken the same number of photos on their school trip. Lisa has taken 3 times as many photos as Claire and Robert has taken 12 more photos than Claire. How many photos has Claire taken?

Translate the information in the question from “English” to “Math.” L = R L = 3C R = C + 12 We can substitute R for L in the second equation: R = 3C. If R is equal to both 3C and C + 12, we can say 3C = C + 12, and solve for C. 3C = C + 12 2C = 12 C = 6

#### If a store adds 50 chairs to its current inventory, the total number of chairs will be the same as three-halves the current inventory of chairs. If the manager wants to increase the current inventory by 40%, what will the new inventory of chairs be?

This word problem requires careful translation. Let’s say t = total current inventory of chairs. The first sentence states that 50 + t = (3/2)t. First solve for the current inventory: 50 + t = (3/2)t 50 = (3/2)t − t 50 = (1/2)t 100 = t The manager wants to increase this by 40%. 40% of 100 is 40, so the new inventory will be 140.

#### The first four terms in a sequence are shown below. What is the sixth term in the sequence?

Begin by examining the sequence for a pattern. In order to go from 3 to 6, 3 must be added; moving from 6 to 11 requires 5 to be added; moving from 11 to 18 requires 7 to be added. The pattern emerges here — adding by consecutive odd integers. The 5th term is equal to 18 + 9 = 27, and the 6th term is equal to 27 + 11 = 38.

#### The absolute value of 5 plus a number equals 10. Which of the following options is the correct solution set for the above equation?

The absolute value of 5 plus a number equals 10” should be written as |5 + x| = 10. Absolute value means the distance of a number from zero, so whenever you solve for the number inside absolute value bars, you must consider both the positive and negative values. Take away the bars and set the expression equal to both 10 and -10. 5 + x = 10 gives you x = 5, and 5 + x = -10 gives you x = -15. The solution set is x = {-15, 5}.

#### Each year, a cyber café charges its customers a base rate of $25, with an additional $0.30 per visit for the first 50 visits, and $0.10 for every visit after that. How much does the cyber café charge a customer for a year in which 72 visits are made?

Translate the information into arithmetic. The café charges $25 + $0.30(first 50) + $0.10(additional after 50). For 72 visits there are 50 visits with an additional 22 visits. $25 + $0.30(50) + $0.10(22) =$25 +$15 + $2.20 =$42.20

#### Which of the following is equivalent to 2 times the total of x plus y?

2 times the total of x plus y is 2(x + y). From there, use the Distributive Property to multiply the 2 by each term inside the parenthesis. 2(x + y) = 2x + 2y

#### If Jill needed to buy 9 bottles of soda for a party in which 12 people attended, how many bottles of soda will she need to buy for a party in which 8 people are attending?

We can set up a proportion to solve: 9 bottles / 12 people = x bottles / 8 people. Cross-multiply to solve a proportion: (9)(8) = (12)(x) 72 = 12x 6 = x

#### Which of the following expressions is equal to 3^{8} when *p* = 3^{5}?

3^{8} = 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3, or 3^{5} x 3^{3} = *p* x 3^{3}

*p* x 3^{3} = 27*p*

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#### With what number must 3.475817 be multiplied in order to obtain the number 34,758.17?

The decimal must be moved four places to the right. To do this, we must multiply by a number with four zeroes. The correct answer is 10,000.

#### If y + 3y + 5y = −18, then what is the value of y?

When terms with the same variable are in the same equation, they can be combined. y + 3y + 5y = 7y 9y = −18 y = −18/9 y = −2

#### If b does not equal zero, and ab = b/4, what is the value of a?

To solve for a, divide both sides of the equation by b: ab = b/4 (ab)/b = (b/4)/b a = (b/4)*1/b a = 1/4

#### The sum of 7 numbers is greater than 140 and less than 210. Which of the following could be the average (arithmetic mean) of the numbers?

The formula for the average of a set of numbers is the sum of the numbers divided by the number of terms. Avg = 140 / 7 Avg = 20 Avg = 210 / 7 Avg = 30 Therefore, the sum must be between 20 and 30.

#### The hour hand of a watch rotates 30 degrees every hour. How many complete rotations does the hour hand make in 6 days?

There are 360 degrees in a complete circle, so 360/30 = 12 hours to make one full circle. In 6 days there are 24 hours x 6 = 144 hours total. The total number of rotations will be 144/12 = 12.

#### How much greater is the value of 3x + 5 than the value of 3x − 7?

The easiest way to do this is to pick a number for x. Let’s say x = 3. 3(3) + 5 = 9 + 5 = 14 3(3) − 7 = 9 − 7 = 2 The correct answer is 14 − 2 = 12.

#### Steve bought a total of 6 packages of pens, and each package contained either 3 or 7 pens. If exactly 4 of the packages Steve bought contained 7 pens, how many pens did Steve buy?

If Steve bought 4 packages of 7 pens and 6 packages total, then he must have purchased 2 packages of 3 pens. 4(7) + 2(3) = 28 + 6 = 34

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