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What is the remainder when the positive integer n is divided

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by BTGmoderatorDC » Fri Feb 08, 2019 5:39 am

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Difficulty—

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

OA B

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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Fri Feb 08, 2019 6:07 am
BTGmoderatorDC wrote: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
Target question: What is the remainder when the positive integer n is divided by 6?

Statement 1: n is multiple of 5
Let's TEST some values.
There are several values of n that satisfy statement 1. Here are two:
Case a: n = 10. In this case, the answer to the target question is the remainder is 4 when n is divided by 6
Case b: n = 15. In this case, the answer to the target question is the remainder is 3 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
If n is a multiple of 12, then we can write: n = 12k for some integer k
If n = 12k, we can also write: n = (6)(2)k, which tells us n is a multiple of 6
If n is a multiple of 6, then n divided by 6 will leave remainder 0
So, the answer to the target question is the remainder is 0 when n is divided by 6
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

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by GMATGuruNY » Fri Feb 08, 2019 7:46 am
BTGmoderatorDC wrote: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
Statement 1:
If n=5, then the remainder when n is divided by 6 = 5/6 = 0 R5.
If n=10, then the remainder when n is divided by 6 = 10/6 = 1 R4.
Since different remainders are possible, INSUFFICIENT.

Statement 2:
Since n is a multiple of 12, n must also be a multiple of 6, with the result that dividing n by 6 will yield a remainder of 0.
SUFFICIENT.

The correct answer is B.
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