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02 Jul 2008, 04:42
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If r is the remainder when the positive integer n is divided by 7, what is the value of r?
(1) When r is divided by 21, the remainder is an odd number.
(2) When n is divided by 28, the remainder is 3.
n = 7x + r
according to (1):
n = 21y + r1 (r1 is odd)
n = 7(3y) + r1
meaning the remainder while dividing by 21 and by 7 is the same odd number, but we don't have a way to find it.
according to (2):
n = 28y + 3
n = 7(4y) + 3
therefore r = 3, and (2) is sufficient.
Is my reasoning correct, is there a better way to explain it? Of course, we don't to explain in the GMAT, but I want to make sure my understanding is correct.
(1) When r is divided by 21, the remainder is an odd number.
(2) When n is divided by 28, the remainder is 3.
n = 7x + r
according to (1):
n = 21y + r1 (r1 is odd)
n = 7(3y) + r1
meaning the remainder while dividing by 21 and by 7 is the same odd number, but we don't have a way to find it.
according to (2):
n = 28y + 3
n = 7(4y) + 3
therefore r = 3, and (2) is sufficient.
Is my reasoning correct, is there a better way to explain it? Of course, we don't to explain in the GMAT, but I want to make sure my understanding is correct.
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nirimblf
Nope, r and r1 are not necessarily the same. Don't forget :
n = 7x + r, with r between 0 and 6 (inclusive)
n = 21y + r1, with r1 between 0 and 20 (inclusive)
We could have r1=17, which is odd and though r won't be equal to 17 then (but 17-2*7 = 3)
That being said, it its true that you don't know much about r1 and therefore don't know much about r (all you can say is that it is odd too, so r belongs to {1,3,5})
For instance :
n = 26 ==> r1 = 5 and r=5
n = 38 ==> r1 = 17 and r=3
==> (1) is insufficient
02 Jul 2008, 04:51
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nirimblf
well you really dont need to get into calculations here, we know r < 7 so the reminder of r/21 is "r" for sure and r being odd r can be 1,3,5 (NOT sufficient)
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good approach i think..
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