What is the remainder when integer n is divided by 10?

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BTGModeratorVI: Legendary Member; Posts: 1223; Joined: Sat Feb 15, 2020 2:23 pmFollowed by: 1 member

by BTGModeratorVI » Thu Aug 27, 2020 12:22 pm

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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.

Answer: D
Source: Princeton Review

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Source: Beat The GMAT — Data Sufficiency | Thu Aug 27, 2020 12:22 pm

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

by Brent@GMATPrepNow » Thu Aug 27, 2020 4:34 pm

BTGModeratorVI wrote: ↑
Thu Aug 27, 2020 12:22 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.

Answer: D
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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swerve: Legendary Member; Posts: 2539; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

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

by swerve » Sat Aug 29, 2020 6:08 pm

BTGModeratorVI wrote: ↑
Thu Aug 27, 2020 12:22 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.

Answer: D
Source: Princeton Review

From statement (1)

$n$ can be $75, 185, 295, 405$ and so on

From statement (2)

$n$ can be $25, 125, 225, 325, 425$ and so on

In both cases, $\dfrac{n}{10}$ will leave a remainder of $5\Longrightarrow$ D

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