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What is the remainder when integer \(n\) is divided by 10?

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Source: — Data Sufficiency |

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Re: What is the remainder when integer \(n\) is divided by 10?

by Brent@GMATPrepNow » Mon Jun 01, 2020 8:47 am

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Gmat_mission wrote: ↑
Sun May 31, 2020 1:25 pm
 What is the remainder when integer \(n\) is divided by 10?

(1) When \(n\) is divided by 110 the remainder is 75.
(2) When \(n\) is divided by 100 the remainder is 25.

[spoiler]OA=D[/spoiler]

Source: Princeton Review
Target question: What is the remainder when integer n is divided by 10?

REPHRASED target question: What is the UNITS DIGIT of n?

Statement 1: When n is divided by 110 the remainder is 75.
In other words: n = 110k + 75 (for some integer k)
Since 110k will have units digit 0 for ANY integer k, we know that 110k + 75 MUST have a units digit of 5
In other words, n MUST have a units digit of 5
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: When n is divided by 100 the remainder is 25
In other words: n = 100k + 25 (for some integer k)
Since 100k will have units digit 0 for ANY integer k, we know that 100k + 25 MUST have a units digit of 5
In other words, n MUST have a units digit of 5
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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