Consider two positive integers, P and Q, where n represents the decimal value of the fraction P/Q. Which of the following conditions must ensure that n is a finite decimal?
I. P = 60, Q = 225
II. Q = 40
III. P = 90, Q = 500

Answer Choices

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None

I only

II only

III only

II & III

Correct

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Explanation

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Official Explanation

Official

To determine if n is a finite decimal, we need to check the prime factorization of Q. A fraction P/Q will have a finite decimal representation if Q has no prime factors other than 2 and 5. For I, Q = 225 = 3^2 *…

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Comments

ThorAug 13, 2024

Great question!

What this question tests

What it tests

Your fluency with the order of operations, fractions, decimals, and basic number sense — the foundation every quant question leans on.

Common trap

Applying the order of operations out of sequence or rounding intermediate values before the final step.

Consider two positive integers, P and Q, where n represents the decimal value of the fraction P/Q. Which of the following conditions must ensure that n is a finite decimal? I. P = 60, Q = 225 II. Q = 40 III. P = 90, Q = 500