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What is the remainder when the positive integer \(n\) is

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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Tue Aug 06, 2019 10:48 pm

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BTGmoderatorLU wrote:Source: GMAT Prep

What is the remainder when the positive integer \(n\) is divided by 6?

1) \(n\) is multiple of 5.
2) \(n\) is a multiple of 12.

The OA is B
Let's take each statement one by one.

1) \(n\) is multiple of 5.

Case 1: Say n= 30, then n is divided by 6. The answer is yes.
Case 2: Say n= 25, then n is NOT divided by 6. The answer is no.

No unique answer. Insufficient.

2) \(n\) is a multiple of 12.

Since \(n\) is a multiple of 12, and 12 is divisible bt 6, we can conclude that n is divided by 6. The answer is yes.

The correct answer: B

Hope this helps!

-Jay
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by Brent@GMATPrepNow » Wed Aug 07, 2019 7:45 am

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BTGmoderatorLU wrote:Source: GMAT Prep

What is the remainder when the positive integer \(n\) is divided by 6?

1) \(n\) is multiple of 5.
2) \(n\) is a multiple of 12.

The OA is B
Target question: What is the remainder when a positive integer n is divided by 6?

Statement 1: n is a multiple of 5
There are several values of n that satisfy this condition. Here are two:
Case a: n = 5, in which case the remainder is 5, when n is divided by 6
Case b: n = 10, in which case the remainder is 4, when n is divided by 6
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: n is a multiple of 12
In other words, n = 12k for some integer k
We can rewrite this as n = (6)(2)k for some integer k
From this, we can see that n is a multiple of 6, which means the remainder must equal 0, when n is divided by 6
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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