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# If x and y are positive integers, which of the following

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Manager
Joined: 11 Apr 2009
Posts: 157
If x and y are positive integers, which of the following [#permalink]

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20 May 2009, 16:19
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If x and y are positive integers, which of the following CANNOT be the greatest common divisor of 35x and 20y?
A. 5
B. 5(x – y)
C. 20x
D. 20y
E. 35x

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Manager
Status: Stanford GSB
Joined: 02 Jun 2008
Posts: 93

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21 May 2009, 00:22
35x/choice and 20y/choice will be an integer.

(a) 5: goes into both 35 and 20, so definitely a divisor of both. Could it be the GCD of both? Sure, let x=y=1 and 5 is the GCD of 35 and 20.

(b) 5(x-y): does it have to go into both? No, but can we make it go into both? Sure: if we pick x=2 and y=1, then we're left with 5(1) = 5, which is the GCD of 70 and 20.

(c) 20x: 20x CANNOT possibly be a factor of 35x, since if we write it as a fraction we get:

35x/20x = 35/20 = 7/4 which isn't an integer.

Therefore, 20x CANNOT possibly be the GCD of 35x and 20y.

Source: Stuart Kovinsky
GMAT Tutor
Joined: 24 Jun 2008
Posts: 1346

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21 May 2009, 06:50
sandipchowdhury wrote:

(b) 5(x-y): does it have to go into both? No, but can we make it go into both? Sure: if we pick x=2 and y=1, then we're left with 5(1) = 5, which is the GCD of 70 and 20.

The solution is correct, except for a small error in the above; the GCD of 20 and 70 is not 5; it's 10. Still, if we choose x=3 and y=2, we can see that 5(x-y) can be the GCD here, so B is not the correct answer.

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Re: MGMAT- GCD   [#permalink] 21 May 2009, 06:50
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