ASVAB Arithmetic Reasoning Practice Test 314772 Results

Your Results Global Average
Questions 5 5
Correct 0 3.17
Score 0% 63%

Review

1

In a class of 28 students, 15 are taking German and 6 are taking Spanish. Of the students studying German or Spanish, 5 are taking both courses. How many students are not enrolled in either course?

63% Answer Correctly
23
12
14
17

Solution

The number of students taking German or Spanish is 15 + 6 = 21. Of that group of 21, 5 are taking both languages so they've been counted twice (once in the German group and once in the Spanish group). Subtracting them out leaves 21 - 5 = 16 who are taking at least one language. 28 - 16 = 12 students who are not taking either language.


2

Find the average of the following numbers: 8, 4, 10, 2.

74% Answer Correctly
1
6
9
4

Solution

To find the average of these 4 numbers add them together then divide by 4:

\( \frac{8 + 4 + 10 + 2}{4} \) = \( \frac{24}{4} \) = 6


3

What is \( \frac{4}{3} \) - \( \frac{7}{5} \)?

61% Answer Correctly
1 \( \frac{7}{15} \)
2 \( \frac{3}{15} \)
-\(\frac{1}{15}\)
\( \frac{1}{15} \)

Solution

To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 3 are [3, 6, 9, 12, 15, 18, 21, 24, 27, 30] and the first few multiples of 5 are [5, 10, 15, 20, 25, 30, 35, 40, 45, 50]. The first few multiples they share are [15, 30, 45, 60, 75] making 15 the smallest multiple 3 and 5 share.

Next, convert the fractions so each denominator equals the lowest common multiple:

\( \frac{4 x 5}{3 x 5} \) - \( \frac{7 x 3}{5 x 3} \)

\( \frac{20}{15} \) - \( \frac{21}{15} \)

Now, because the fractions share a common denominator, you can subtract them:

\( \frac{20 - 21}{15} \) = \( \frac{-1}{15} \) = -\(\frac{1}{15}\)


4

A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 15% off." If Frank buys two shirts, each with a regular price of $20, how much will he pay for both shirts?

57% Answer Correctly
$28.00
$37.00
$26.00
$29.00

Solution

By buying two shirts, Frank will save $20 x \( \frac{15}{100} \) = \( \frac{$20 x 15}{100} \) = \( \frac{$300}{100} \) = $3.00 on the second shirt.

So, his total cost will be
$20.00 + ($20.00 - $3.00)
$20.00 + $17.00
$37.00


5

Simplify \( \sqrt{48} \)

62% Answer Correctly
5\( \sqrt{6} \)
9\( \sqrt{6} \)
4\( \sqrt{3} \)
6\( \sqrt{6} \)

Solution

To simplify a radical, factor out the perfect squares:

\( \sqrt{48} \)
\( \sqrt{16 \times 3} \)
\( \sqrt{4^2 \times 3} \)
4\( \sqrt{3} \)