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GMAT Prep ?? Another divisibility Pract 2

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by dferm » Tue May 13, 2008 4:26 pm
If r is the remainder when the positive integer n is divided by 7, what is the value of r?

(1) When n is divided by 21, the remainder is an odd number
(2) When n is divided by 28, the remainder is 3

Please Help..

Thanks.
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Source: — Data Sufficiency |
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by rosenjon » Tue May 13, 2008 4:55 pm
First let's take a look at the stem. While it defines some variables, it doesn't really help you out much. We want to know the remainder when an unknown number is divided by 7. So basically, we are starting from scratch here, with the exception that we know that r<=6

Statement 1 doesn't help much. It could really be anything. You can prove this by choosing different numbers for N (n=22, n=24, n=28, etc)

Cross off AD.

Statement 2 is more concrete.

It can be rewritten as: n = 28(c) + 3

So plug in numbers for c:

c =1, so n = 31
c = 2, so n = 59
c = 3, so n = 87

31/7 = 4r3
59/7 = 8r3
87/7 = 12r3

We can see that we get a remainder of 3 in every case. This is sufficient to answer the stem. So the answer is B.
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