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If X and Y are positive integers, what is the remainder of

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CEO
CEO
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Joined: 21 Jan 2007
Posts: 2760
Location: New York City
Followers: 9

Kudos [?]: 423 [0], given: 4

If X and Y are positive integers, what is the remainder of [#permalink] New post 07 Nov 2007, 08:53
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If X and Y are positive integers, what is the remainder of (XY)/4?

1. remainder of x/4 is 3
2. remainder of y/4 is 2
Manager
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Joined: 25 Jul 2007
Posts: 108
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Kudos [?]: 15 [0], given: 0

 [#permalink] New post 07 Nov 2007, 09:14
Statement 1 tells us that possible values of X are 3,7,11,15......Not Sufficient

Statement 2 tells us that possible values of Y are 2,6,10,14......Not Sufficient

Combining both the statements, we find that the product of any possible value of X and any possible value of Y leaves a remainder of 2 when divided by 4.....e.g: 3*2,11*14,...

Therefore, C is the answer.

A more conceptual approach is as follows:
X=4n+3
Y=4m+2

Therefore,
XY=(4n+3)(4m+2)
= 16nm+8n+12m+6
= 16nm+8n+12m+4+2
= 4(4nm+2n+3m+1) + 2

Therefore (XY)/4 will always leave a remainder of 2.
  [#permalink] 07 Nov 2007, 09:14
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If X and Y are positive integers, what is the remainder of

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