ASVAB Math Test Prep

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Question 1 |

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

100 | |

1,000 | |

10,000 | |

100,000 |

Question 1 Explanation:

The correct answer is (C). 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.

Question 2 |

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

8 | |

10 | |

12 | |

14 |

Question 2 Explanation:

The correct answer is (C). 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: $14 − 2 = 12$

$3(3) + 5$

$= 9 + 5$

$= 14$

$3(3) − 7$

$= 9 − 7$

$= 2$

The correct answer is: $14 − 2 = 12$

Question 3 |

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

5 | |

6 | |

12 | |

15 |

Question 3 Explanation:

The correct answer is (C). A factor must divide evenly into its multiple. We know 12 cannot be a factor of 90 because:

$90 ÷ 12 = 7.5$

$90 ÷ 12 = 7.5$

Question 4 |

### 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?

6 | |

8 | |

10 | |

12 |

Question 4 Explanation:

The correct answer is (A). 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

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

Question 5 |

### 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?

20 | |

26 | |

30 | |

34 |

Question 5 Explanation:

The correct answer is (B). 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.

Avg = 140 ÷ 7

Avg = 20

Avg = 210 ÷ 7

Avg = 30

Therefore, the sum must be between 20 and 30.

Question 6 |

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

8 | |

10 | |

12 | |

14 |

Question 6 Explanation:

The correct answer is (C). 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 × 6 = 144 hours total. The total number of rotations will be 144 ÷ 12 = 12.

Question 7 |

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

6 p | |

9 p | |

16 p | |

27 p |

Question 7 Explanation:

The correct answer is (D).

3

3

^{8}= 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3, or 3^{5}× 3^{3}=*p*× 3^{3}*p*x 3^{3}= 27*p*Question 8 |

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

−2 | |

−1 | |

0 | |

1 |

Question 8 Explanation:

The correct answer is (A). When terms with the same variable are in the same equation, they can be combined:

$y + 3y + 5y = −18$

$9y = −18$

$y = \dfrac{−18}{9}$

$y = −2$

$y + 3y + 5y = −18$

$9y = −18$

$y = \dfrac{−18}{9}$

$y = −2$

Question 9 |

### If $b$ does not equal zero, and $ab = \frac{b}{4}$, what is the value of $a$?

$\dfrac{1}{8}$ | |

$\dfrac{1}{4}$ | |

$\dfrac{1}{3}$ | |

$\dfrac{1}{2}$ |

Question 9 Explanation:

The correct answer is (B). To solve for a, divide both sides of the equation by $b$:

$ab = \dfrac{b}{4}$

$\dfrac{ab}{b} = \dfrac{\frac{b}{4}}{b}$

$a = \dfrac{b}{4} * \dfrac{1}{b}$

$a = \dfrac{1}{4}$

$ab = \dfrac{b}{4}$

$\dfrac{ab}{b} = \dfrac{\frac{b}{4}}{b}$

$a = \dfrac{b}{4} * \dfrac{1}{b}$

$a = \dfrac{1}{4}$

Question 10 |

### 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?

40 | |

60 | |

100 | |

140 |

Question 10 Explanation:

The correct answer is (D). This word problem requires careful translation. Let’s say $t$ = total current inventory of chairs. The first sentence states that $50 + t = \frac{3}{2} t$. First solve for the current inventory:

$50 + t = \dfrac{3}{2} t$

$50 = \dfrac{3}{2} t − t$

$50 = \dfrac{1}{2} t$

$100 = t$

The manager wants to increase this by 40%. We know that 40% of 100 is 40, so the new inventory will be 140.

$50 + t = \dfrac{3}{2} t$

$50 = \dfrac{3}{2} t − t$

$50 = \dfrac{1}{2} t$

$100 = t$

The manager wants to increase this by 40%. We know that 40% of 100 is 40, so the new inventory will be 140.

Question 11 |

### 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?

580 | |

720 | |

960 | |

1140 |

Question 11 Explanation:

The correct answer is (B). 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:

$18 × 40 = 720$

$18 × 40 = 720$

Question 12 |

### How many $\frac{1}{3}$ pound paperback books together weigh 25 pounds?

35 | |

50 | |

60 | |

75 |

Question 12 Explanation:

The correct answer is (D). If each book weighs $\frac{1}{3}$ pound, then 1 pound = 3 books. To find the number of books in 25 pounds, simply multiply this 3 by 25:

$25 × 3 = 75$

$25 × 3 = 75$

Question 13 |

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

### {3, 6, 11, 18, …}

25 | |

27 | |

38 | |

51 |

Question 13 Explanation:

The correct answer is (C). 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 5th term is equal to 18 + 9 = 27, and the 6th term is equal to 27 + 11 = 38.

Question 14 |

### 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?

36.60 | |

42.20 | |

47.80 | |

51.10 |

Question 14 Explanation:

The correct answer is (B). 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.

$= \$25 + \$0.30(50) + \$0.10(22)$

$= \$25 + \$15 + \$2.20$

$= \$42.20$

$= \$25 + \$0.30(50) + \$0.10(22)$

$= \$25 + \$15 + \$2.20$

$= \$42.20$

Question 15 |

### 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?

6 | |

8 | |

10 | |

12 |

Question 15 Explanation:

The correct answer is (A). We can set up a proportion to solve:

$\dfrac{9 \text{ bottles}}{12 \text{ people}} = \dfrac {x \text{ bottles}}{8 \text{ people}}$

Cross-multiply to solve a proportion:

$(9)(8) = (12)(x)$

$72 = 12x$

$6 = x$

$\dfrac{9 \text{ bottles}}{12 \text{ people}} = \dfrac {x \text{ bottles}}{8 \text{ people}}$

Cross-multiply to solve a proportion:

$(9)(8) = (12)(x)$

$72 = 12x$

$6 = x$

Question 16 |

### 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?

17 | |

21 | |

34 | |

42 |

Question 16 Explanation:

The correct answer is (C). If Steve bought 4 packages of 7 pens and 6 packages total, then he must have purchased 2 packages of 3 pens.

$4(7) + 2(3) = 28 + 6 = 34$

$4(7) + 2(3) = 28 + 6 = 34$

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