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Any decimal that has only a finite number of nonzero digits

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Any decimal that has only a finite number of nonzero digits

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Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 24, 0.82, and 5.096 are three terminating decimals. If r and s are positive integers and the ratio r/s is expressed as a decimal, is r/s a terminating decimal?

(1) 90 < r < 100
(2) s = 4

OA B

Source: Official Guide

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BTGmoderatorDC wrote:
Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 24, 0.82, and 5.096 are three terminating decimals. If r and s are positive integers and the ratio r/s is expressed as a decimal, is r/s a terminating decimal?

(1) 90 < r < 100
(2) s = 4

OA B

Source: Official Guide
Target question: Is r/s a terminating decimal?

Statement 1: 90 < r < 100
There are several pairs of values that meet this condition. Here are two:
Case a: r = 91 and s = 2, in which case r/s = 91/2 = 45.5 = a terminating decimal
Case b: r = 91 and s = 3, in which case r/s = 91/3 = 30.33333.... = a non-terminating decimal
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: s = 4
Notice that 1/4 = 0.25, 2/4 = 0.5 and 3/4 = 0.75
So, if the denominator is 4, the resulting decimal will definitely be a terminating decimal.
In other words, if s = 4 then r/s must be a terminating decimal.
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Aside: There's a nice rule that says something like,
If the prime factorization of the denominator contains only 2's and/or 5's, then the decimal version of the fraction will be a terminating decimal.
Since the denominator, 4 = (2)(2), the rule tells us that r/s must be a terminating decimal.

Answer: B

Cheers,
Brent

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