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# If r is the remainder when positive integer n is divided by

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Manager
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If r is the remainder when positive integer n is divided by [#permalink]  18 Sep 2006, 16:43
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If r is the remainder when 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

Senior Manager
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Re: GMAT Prep - number properties DS [#permalink]  18 Sep 2006, 16:55
wshaffer wrote:
If r is the remainder when 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

24/21 r=3 24/7 r=3, but 26/21 r=5 26/7 r=5 both are odd - INSUFF

31/28 r=3 31/7 r=3 SUFF (i.e. when n is divided by 28 and r=3, then same result is for when n is divided by 7, since 28 is multiple of 7)
Senior Manager
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B for me

I assume that 28 is a multiply of 7 and will hence have the same remainder. 21 is also a multiple but the it just says that r is odd (not a specific number).

If this the correct reasoning?
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Another way

I
22/21 r = 1
24/21 r = 3
Insufficient

II
n/28 r = 3 - realize that 7 is a factor of 28
31/7 r = 3

Sufficient
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If r is the remainder when 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

if n=7q+r what is r

n=21x+(2k+1) where k is any positive intiger when this is devided by 7

21x/7 = 3x

2k+1 = depends on values of k...insuff

from two

n = 28z+3 when this is devided by 7

287/7 = 4z

3/7 = 3....suff

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