ASVAB Arithmetic Reasoning Practice Test 796740 Results

Your Results Global Average
Questions 5 5
Correct 0 3.23
Score 0% 65%

Review

1

Solve for \( \frac{2!}{6!} \)

67% Answer Correctly
20
\( \frac{1}{360} \)
336
504

Solution

A factorial is the product of an integer and all the positive integers below it. To solve a fraction featuring factorials, expand the factorials and cancel out like numbers:

\( \frac{2!}{6!} \)
\( \frac{2 \times 1}{6 \times 5 \times 4 \times 3 \times 2 \times 1} \)
\( \frac{1}{6 \times 5 \times 4 \times 3} \)
\( \frac{1}{360} \)


2

Simplify \( \frac{28}{64} \).

77% Answer Correctly
\( \frac{8}{17} \)
\( \frac{6}{13} \)
\( \frac{7}{16} \)
\( \frac{4}{19} \)

Solution

To simplify this fraction, first find the greatest common factor between them. The factors of 28 are [1, 2, 4, 7, 14, 28] and the factors of 64 are [1, 2, 4, 8, 16, 32, 64]. They share 3 factors [1, 2, 4] making 4 their greatest common factor (GCF).

Next, divide both numerator and denominator by the GCF:

\( \frac{28}{64} \) = \( \frac{\frac{28}{4}}{\frac{64}{4}} \) = \( \frac{7}{16} \)


3

Which of these numbers is a factor of 24?

68% Answer Correctly
14
11
1
17

Solution

The factors of a number are all positive integers that divide evenly into the number. The factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24.


4

A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 10% off." If Ezra buys two shirts, each with a regular price of $50, how much money will he save?

70% Answer Correctly
$7.50
$10.00
75
$5.00

Solution

By buying two shirts, Ezra will save $50 x \( \frac{10}{100} \) = \( \frac{$50 x 10}{100} \) = \( \frac{$500}{100} \) = $5.00 on the second shirt.


5

What is 7\( \sqrt{4} \) x 2\( \sqrt{3} \)?

41% Answer Correctly
9\( \sqrt{3} \)
28\( \sqrt{3} \)
14\( \sqrt{4} \)
9\( \sqrt{4} \)

Solution

To multiply terms with radicals, multiply the coefficients and radicands separately:

7\( \sqrt{4} \) x 2\( \sqrt{3} \)
(7 x 2)\( \sqrt{4 \times 3} \)
14\( \sqrt{12} \)

Now we need to simplify the radical:

14\( \sqrt{12} \)
14\( \sqrt{3 \times 4} \)
14\( \sqrt{3 \times 2^2} \)
(14)(2)\( \sqrt{3} \)
28\( \sqrt{3} \)