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Numbers-Factors and multiples.

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by Brent@GMATPrepNow » Sat Nov 14, 2015 2:55 pm
imran556691 wrote:This is confusing.What is the approach to solve this?Please help


If 2n is a multiple of 7, which of the following should be multiples of 7 ?


A. 4n
B. 7n
C. n/2
D. 6n
E. 7n/4
Should be multiples of 7?
Do you mean MUST be a multiple of 7?

If 2n is a multiple of 7, then 2n = 7k for some integer k.

Now check the answer choices:

A. 4n = 2(2n) = 2(7k) = 7(2k). So, we can write 4n as a multiple of 7.
Answer: A

But hold on...
D. 6n = 3(2n) = 3(7k) = 7(3k). So, we can write 6n as a multiple of 7.
Answer: D

Hmmmm, two correct answers. Not good.
What's the source of this question?

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Brent
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by [email protected] » Sat Nov 14, 2015 6:21 pm
Hi imran556691,

This prompt has 2 correct answers. Is it meant to be a GMAT question or a general 'concept' question?

We're told that 2N is a MULTIPLE of 7, so 2N could be 0, 7, 14, 21, 28, 35.....

By extension, N could be 0, 3.5, 7, 10.5, 14, 17.5....

Since we don't know WHICH multiple of 7 we're dealing with, we have to consider a few possibilities to see if a pattern occurs...

IF N = 0, then all of the answers are multiples of 7.
IF N = 3.5, then Answers A and D are multiples of 7.
IF N = 7, then A, B and D are multiples of 7.
IF N = 10.5, then A and D are multiples of 7.

Based on the above examples, only Answers A and D will ALWAYS be a multiple of 7.

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