Practice USAT Quantitative Reasoning questions with answers and explanations.
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Dividing 84 by primes gives 84 = 2 × 2 × 3 × 7.
This is 2² × 3 × 7.
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Since 12 × 13 = 156, subtracting gives 157 - 156 = 1.
Thus, the remainder is 1.
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Division and multiplication have equal priority and are performed left to right.
So 48 ÷ 6 = 8, and 8 × 3 = 24.
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The digit 7 is in the thousands place.
Therefore, its place value is 7 × 1,000 = 7,000.
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A prime number has exactly two positive factors: 1 and itself.
The number 29 is not divisible by 2, 3, or 5.
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The common factors of 36 and 48 include 1, 2, 3, 4, 6, and 12.
The greatest of these is 12.
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Multiples of 8 are 8, 16, 24, and so on.
The first multiple also divisible by 12 is 24.
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A number is divisible by 9 when the sum of its digits is divisible by 9.
For 5,832, the digit sum is 18.
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An irrational number cannot be expressed as a ratio of integers.
The number √2 has a nonterminating, nonrepeating decimal expansion.
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The expression 2⁵ means multiplying five factors of 2.
Thus, 2 × 2 × 2 × 2 × 2 = 32.
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The square root is the number whose square equals 196.
Since 14 × 14 = 196, the answer is 14.
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The cube root is the number that gives 729 when cubed.
Since 9³ = 729, the answer is 9.
