Practice USAT Quantitative Reasoning questions with answers and explanations.
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The sum of the first n natural numbers is n(n + 1)/2.
For n = 10, the sum is 10 × 11 ÷ 2 = 55.
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The sum of the first n odd numbers equals n².
For n = 8, the sum is 8² = 64.
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The least common multiple of 3 and 4 is 12.
A number divisible by both must therefore be divisible by 12.
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The units digits of powers of 7 cycle as 7, 9, 3, 1.
The fourth power therefore ends in 1.
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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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Multiplication is performed before addition.
Thus, 3 × 4 = 12 and 5 + 12 = 17.
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The operation inside parentheses is completed first.
Then 12 ÷ 3 = 4.
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The multiplicative inverse of a nonzero fraction is its reciprocal.
Interchanging numerator and denominator gives 7/5.
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A composite number has more than two positive factors.
The number 4 has factors 1, 2, and 4.
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The positive factors of 16 are 1, 2, 4, 8, and 16.
Therefore, it has 5 positive factors.
