ASVAB Arithmetic Reasoning Test 1 — Questions and Answers

Question 1: With what number must 3.475817 be multiplied in order to obtain the number 34,758.17?

100
1,000
10,000 (Correct answer)
100,000

Correct answer: 10,000

To transform 3.475817 into 34,758.17, the decimal point needs to be moved four places to the right. Each shift of the decimal point one place to the right corresponds to multiplying by 10. Therefore, moving it four places to the right means multiplying by 10 x 10 x 10 x 10, which equals 10,000.

Question 2: How much greater is the value of 3x + 5 than the value of 3x − 7?

8
10
12 (Correct answer)
14

Correct answer: 12

To find how much greater one expression is than another, subtract the second expression from the first: (3x + 5) - (3x - 7). Distributing the negative sign gives 3x + 5 - 3x + 7. The '3x' terms cancel out, leaving 5 + 7, which simplifies to 12. Thus, 3x + 5 is 12 greater than 3x - 7.

Question 3: Which of the following is NOT a factor of 90?

5
6
12 (Correct answer)
15

Correct answer: 12

A factor of a number divides into that number evenly, with no remainder. We can check each option: 90/5 = 18, 90/6 = 15, and 90/15 = 6, so 5, 6, and 15 are all factors of 90. However, 90 divided by 12 results in 7.5, which is not an integer. Therefore, 12 is not a factor of 90.

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 (Correct answer)
8
10
12

Correct answer: 6

Let C represent the number of photos Claire took. Lisa took 3 times as many as Claire, so Lisa took 3C photos. Robert took 12 more photos than Claire, so Robert took C + 12 photos. Since Lisa and Robert took the same number of photos, we set their expressions equal: 3C = C + 12. Subtracting C from both sides gives 2C = 12, and dividing by 2 yields 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 (Correct answer)
30
34

Correct answer: 26

The average (arithmetic mean) of a set of numbers is their sum divided by the count of numbers. Given that the sum of 7 numbers is greater than 140 and less than 210, the average must be between 140/7 and 210/7. This means the average must be greater than 20 and less than 30. Of the given options, only 26 falls within this range.

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 (Correct answer)
14

Correct answer: 12

The hour hand completes one full 360-degree rotation every 12 hours. In 6 days, there are 6 * 24 = 144 hours in total. To find the number of complete rotations, divide the total hours by the hours it takes for one rotation: 144 hours / 12 hours/rotation = 12 rotations. So, the hour hand makes 12 complete rotations in 6 days.

Question 7: Which of the following expressions is equal to 38 when p = 35?

6p
9p
16p
27p (Correct answer)

Correct answer: 27p

We are given p = 3^5 and need to find an expression equal to 3^8. We can rewrite 3^8 using the properties of exponents as 3^(3+5), which is equivalent to 3^3 * 3^5. Since 3^3 equals 27, and we know p = 3^5, we can substitute p into the expression, resulting in 27 * p, or 27p.

Question 8: If y + 3y + 5y = −18, then what is the value of y?

−2 (Correct answer)
−1
0
1

Correct answer: −2

First, combine the like terms on the left side of the equation: y + 3y + 5y simplifies to 9y. The equation then becomes 9y = -18. To solve for y, divide both sides of the equation by 9. This gives y = -18 / 9, which results in y = -2.

Question 9: If b does not equal zero, and ab = b/4, what is the value of a?

1/8
1/4 (Correct answer)
1/3
1/2

Correct answer: 1/4

To find the value of 'a', we need to isolate 'a' in the given equation `ab = b/4`. Since 'b' does not equal zero, we can divide both sides of the equation by 'b'. This simplifies the equation to `a = (b/4) / b`, which further reduces to `a = 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 (Correct answer)

Correct answer: 140

First, set up an equation to find the current inventory (C). The problem states that C + 50 = (3/2)C, which solves to C = 100 chairs. Next, calculate the new inventory by increasing the current inventory by 40%. This is done by multiplying the current inventory by 1.40 (representing 100% + 40%), so 100 * 1.40 = 140 chairs.

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 (Correct answer)
960
1140

Correct answer: 720

To find the actual distance, first determine how many '1/4 inch' segments are contained within the 18-inch map measurement. Dividing 18 by 1/4 gives 72 segments. Since each 1/4 inch segment represents 10 miles, multiply 72 by 10 to get the total actual distance of 720 miles.

Question 12: How many 1/3 pound paperback books together weigh 25 pounds?

35
50
60
75 (Correct answer)

Correct answer: 75

To find out how many books are needed, divide the total desired weight by the weight of a single book. The total weight is 25 pounds, and each book weighs 1/3 pound. Dividing 25 by 1/3 is equivalent to multiplying 25 by the reciprocal of 1/3, which is 3. Therefore, 25 * 3 = 75 books.

Question 13: The first four terms in a sequence are shown below. What is the sixth term in the sequence?

25
27
38 (Correct answer)
51

Correct answer: 38

Assuming the sequence provided in the original question was 3, 6, 11, 18, the pattern involves adding consecutive odd numbers: +3, +5, +7. Following this pattern, the fifth term would be 18 + 9 = 27. The sixth term would then be 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 (Correct answer)
47.80
51.10

Correct answer: 42.20

Calculate the total cost by summing the base rate and the costs for different tiers of visits. The base rate is $25. The first 50 visits cost $0.30 each, totaling $15 (50 * $0.30). The remaining 22 visits (72 - 50) cost $0.10 each, totaling $2.20. Adding these amounts together ($25 + $15 + $2.20) gives a total charge of $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 (Correct answer)
8
10
12

Correct answer: 6

This is a direct proportion problem. Set up a ratio of bottles to people: 9 bottles for 12 people. To find out how many bottles are needed for 8 people, set up the proportion 9/12 = x/8. Cross-multiply and solve for x: 9 * 8 = 12 * x, which simplifies to 72 = 12x. Dividing 72 by 12 yields x = 6 bottles.

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 (Correct answer)
42

Correct answer: 34

First, calculate the number of pens from the packages containing 7 pens. Since 4 packages had 7 pens each, that's 4 * 7 = 28 pens. Next, determine the number of packages containing 3 pens. With 6 total packages and 4 having 7 pens, the remaining 2 packages must have had 3 pens each, totaling 2 * 3 = 6 pens. Finally, add these amounts together (28 + 6) to find the total of 34 pens.

Question 17: Which of the following is equivalent to 2 times the total of x plus y?

2x + 2y (Correct answer)
2x(2y)
2x/2y
2xy

Correct answer: 2x + 2y

The phrase 'the total of x plus y' translates to the expression (x + y). When this total is multiplied by 2, the expression becomes 2(x + y). Applying the distributive property, we multiply 2 by both x and y, resulting in 2x + 2y.

Question 18: The absolute value of 5 plus a number equals 10. Which of the following options is the correct solution set for the above equation?

{-5, 5}
{10, -10}
{-5, 15}
{-15, 5} (Correct answer)

Correct answer: {-15, 5}

The statement 'The absolute value of 5 plus a number equals 10' can be written as |5 + n| = 10. This absolute value equation has two possible solutions. Either (5 + n) = 10, which gives n = 5, or (5 + n) = -10, which gives n = -15. Therefore, the correct solution set for the number is {-15, 5}.

ASVAB Arithmetic Reasoning Test 1

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