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# If x and y are positive integers such that x=8y+12, what is

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Joined: 11 May 2008
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If x and y are positive integers such that x=8y+12, what is [#permalink]

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04 Sep 2008, 20:21
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If x and y are positive integers such that x=8y+12, what is the greatest common divisor of x and y?
(1) x is divisible by 12.
(2) y is divisible by 12.
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Joined: 23 Sep 2007
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04 Sep 2008, 21:23
arjtryarjtry wrote:
If x and y are positive integers such that x=8y+12, what is the greatest common divisor of x and y?
(1) x is divisible by 12.
(2) y is divisible by 12.

B
because statement 2 would result in x=12n, where n is an odd integer, y =12a if a is an even integer, n is not divisible by a, if a is an odd integer, n still will not be divisible by a. thus the GCD is 12.
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Joined: 17 Jun 2008
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05 Sep 2008, 00:38
I used numbers to get the answer B.

Stmt 1: x is divisible by 12...that means two 2's and one 3 is required. In 8y+12, 12 is divisible by 12, but in order for 8y to be divisble by 12, y has to be a multiple of 3.

Thus, y can be 3, 6,9,12,15,18...etc and GCD of x and y can be 3, 6, 12,...etc....not sufficient.

Stmt2: y is divisible by 12....and y is positive....hence y is a multiple of 12

Values of y 12,24,36,48...
Values of x 12X9, 12X17, 12X25, 12X33.....

Thus, GCD between X and Y will be 12. Hence, sufficient.
Senior Manager
Joined: 16 Jul 2008
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05 Sep 2008, 01:06
From the stem, we have that x is divisible by 4 and definitely not divisible by 8 (x divided by 8 gives a remainder of 4). Also, y = (x-12)/8. Therefore x = 4*5; 4*7; 4*9; .... 4 times odd number. Y can be anything. Therefore, Statement 1 cannot be sufficient by itself, becuase it only gives us information on x and not on y.

Jumping straight to statement 2), it gives us that y is divisible by 12. This means that y is at least 12 and x is at least 12*9 and the GCD could be 12.

For y=n*12, x=(8*n+1)*12. No way the GCD is n*12. Answer should be B.
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VP
Joined: 17 Jun 2008
Posts: 1329

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05 Sep 2008, 21:58
scthakur wrote:
I used numbers to get the answer B.

Stmt 1: x is divisible by 12...that means two 2's and one 3 is required. In 8y+12, 12 is divisible by 12, but in order for 8y to be divisble by 12, y has to be a multiple of 3.

Thus, y can be 3, 6,9,12,15,18...etc and GCD of x and y can be 3, 6, 12,...etc....not sufficient.

Stmt2: y is divisible by 12....and y is positive....hence y is a multiple of 12

Values of y 12,24,36,48...
Values of x 12X9, 12X17, 12X25, 12X33.....

Thus, GCD between X and Y will be 12. Hence, sufficient.

good Explanation!!
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Re: GCD   [#permalink] 05 Sep 2008, 21:58
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# If x and y are positive integers such that x=8y+12, what is

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