ASVAB Math Knowledge Practice Test 3: Number Properties, Factors and Roots
- Number Properties, Factors and Roots
- 10 questions
- 12 minutes
This test checks number facts that the Math Knowledge section expects you to know without long calculations: factors and multiples, primes, square roots, exponents and the order of operations.
Tap an option to mark your answer. You can change your mind, or tap the same option again to leave the question blank. The correct answers and explanations appear when you finish the test.Tap an option to answer; tap it again to leave the question blank.
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Question 1
What is the greatest common factor of 36 and 60?
Correct answer: D
The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36, and 12 is the largest of them that also divides 60. The answer 180 is the least common multiple.
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Question 2
What is the least common multiple of 8 and 12?
Correct answer: B
The multiples of 12 are 12, 24, 36 …, and 24 is the first one that 8 also divides. The answer 96 is simply 8 × 12, a common multiple but not the least one; 4 is the greatest common factor.
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Question 3
Which of these numbers is prime?
Correct answer: C
59 has no factors other than 1 and itself. The others only look prime: 51 = 3 × 17, 57 = 3 × 19 and 91 = 7 × 13.
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Question 4
Which expression is equal to 75?
Correct answer: A
Write 75 as 25 × 3. Since 25 = 5, 75 = 53. The answer 253 forgets to take the square root of 25.
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Question 5
What is the value of 20 + 2−1 + 2−2?
Correct answer: B
20 = 1, 2−1 = 12 and 2−2 = 14, so the sum is 1 + 12 + 14 = 74. The answer 34 treats 20 as 0 instead of 1.
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Question 6
Which of these numbers is irrational?
Correct answer: C
20 is not a perfect square, so 20 is a non-ending, non-repeating decimal. 49 = 7, 0.25 = 14 and 37 are all ratios of whole numbers.
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Question 7
How is 0.000452 written in scientific notation?
Correct answer: D
Move the decimal point 4 places to the right to get 4.52, so the power of ten is −4. A positive exponent would make the number larger than 1.
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Question 8
What is the value of 18 − 3 × (4 − 6)2 ÷ 6?
Correct answer: A
Work inside the parentheses first: (−2)2 = 4. Then 3 × 4 ÷ 6 = 2, and 18 − 2 = 16. The answer 10 comes from subtracting 18 − 3 first, before multiplying.
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Question 9
Which number is divisible by both 3 and 4?
Correct answer: D
The digits of 4,512 add up to 12, which is divisible by 3, and its last two digits, 12, are divisible by 4. 2,346 and 5,430 pass the test for 3 but not for 4, and 3,128 passes for 4 but not for 3.
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Question 10
If x3 = −27, what is the value of x2?
Correct answer: B
The only real number whose cube is −27 is x = −3, and (−3)2 = 9. A square of a nonzero real number is never negative, so −9 is impossible; −3 is the value of x, not of x2.
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