ASVAB Arithmetic Reasoning Practice - 7

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

• 100

• 1,000

• 10,000

• 100,000

Answer explanation

The correct answer is 10,000. 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.

Tags

CCSS.5.NBT.A.2

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

• 8

• 10

• 12

• 14

Answer explanation

The correct answer is 12.

The easiest way 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

Tags

CCSS.6.NS.C.7C

Which of the following is NOT a factor of 90?

• 5

• 6

• 12

• 14

Answer explanation

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

90÷12=7.5

Tags

CCSS.4.OA.B.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

Answer explanation

The correct answer is 6. 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

Tags

CCSS.4.OA.A.2

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

Answer explanation

The correct answer is 26. 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.

Tags

CCSS.7.EE.B.3

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

Answer explanation

The correct answer is 12. 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.

Tags

CCSS.7.EE.B.3

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

• 6p

• 9p

• 16p

• 27p

Answer explanation

The correct answer is 27p.

3⁸ = 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3, or 3⁵ × 3³ = p × 3³

p x 3³ = 27p

Tags

CCSS.6.EE.A.1

If y + 3y + 5y = −18,

then what is the value of y?

• -2

• -1

• 0

• 1

Answer explanation

The correct answer is -2. When terms with the same variable are in the same equation, they can be combined:

y+3y+5y=−18

9y=−18

$\frac{9y}{9}=-\frac{18}{9}$

y = -2

Tags

CCSS.7.NS.A.3

If bb does not equal zero, and 

 $ab=\frac{b}{4}$ , what is the value of a? 

•  $\frac{1}{8}$  

•  $\frac{1}{4}$  

•  $\frac{1}{3}$  

•  $\frac{1}{2}$  

Answer explanation

The correct answer is  $\frac{1}{4}$  . 

To solve for a, start by multiplying both sides by 4.
 $4\times ab=\frac{b}{4}\times4$  

 $4ab=b$ 

  $\frac{4ab}{b}=\frac{b}{b}$  

 $4a=1$  

 $\frac{4a}{4}=\frac{1}{4}$  

 $a=\frac{1}{4}$  

Tags

CCSS.8.EE.A.1

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

Answer explanation

The correct answer is 140. This word problem requires careful translation.
Let’s say t = total current inventory of chairs.
The first sentence states that $t+50=\frac{3}{2}t$ .

Solve for t.
$2\times\left(t+50\right)=2\times\frac{3}{2}t$

$2t+100=3t$

$2t+100-2t=3t-2t$

$100=t$

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

Tags

CCSS.7.RP.A.3