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If x and y are both integers greater than 1, is x a multiple [#permalink]
 04 May 2008, 19:26
Question Stats:
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61% (01:24) wrong based on 1 sessions
If x and y are both integers greater than 1, is x a multiple of y? (1) 3y^2 + 7y = x (2) x^2 -x is a multiple of y
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Re: DS: x multiple of y? [#permalink]
04 May 2008, 20:35
chineseburned wrote: If x and y are both integers greater than 1, is x a multiple of y?
(1) 3y^2 + 7y = x
(2) x^2 -x is a multiple of y Hi, it is long time to see you! 1 suff. no discustion 2. x(x-1) is multiple of y. So x may or may not is multiple of y. a. x=5, y = 2 5*6 is multiple of 2, but x=5 is not multiple of 2 b. x=6 6*7 is multiple of 2, and x=6 is multiple of 2
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Re: DS: x multiple of y? [#permalink]
04 May 2008, 20:55
chineseburned wrote: If x and y are both integers greater than 1, is x a multiple of y?
(1) 3y^2 + 7y = x
(2) x^2 -x is a multiple of y A. Given: x > 1 y > 1 n, x, y = integer Asking: Is x = ny? (1) x = y*(3y + 7) Because y is integer, (3y + 7) must be integer; therefore, x must equal integer * y SUFFICIENT (2) x^2 - x = ny Plug in numbers to satisfy above condition... Say x=3, n=1, then y=6. In this case, x is not a multiple of y. Say x=6, n=15, then y=2. In this case, x is a multiple of y. The solution actually depends on what n is, and the only condition we have is n is integer. Therefore, it is INSUFFICIENT
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Re: DS: x multiple of y? [#permalink]
04 May 2008, 21:29
chineseburned wrote: If x and y are both integers greater than 1, is x a multiple of y?
(1) 3y^2 + 7y = x
(2) x^2 -x is a multiple of y (1) 3y^2 + 7y = x y (3y + 7) = x so x must be a multiple, (3y+7) times, of y. suff... (2) x^2 -x is a multiple of y x^2 - x = yk where k is an integer. x (x-1) = yk from this we do not know whether x - 1 or x is equal to k. so nsf.... A.
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Re: DS: x multiple of y? [#permalink]
24 Jun 2008, 18:02
GMAT TIGER wrote:
(2) x^2 -x is a multiple of y
x^2 - x = yk where k is an integer.
x (x-1) = yk
from this we do not know whether x - 1 or x is equal to k. so nsf....
What is the reasoning behind multiplying y by another variable in Statement 2 (in this case k)?
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Re: DS: x multiple of y? [#permalink]
24 Jun 2008, 23:26
AlinderPatel wrote: GMAT TIGER wrote:
(2) x^2 -x is a multiple of y
x^2 - x = yk where k is an integer.
x (x-1) = yk
from this we do not know whether x - 1 or x is equal to k. so nsf....
What is the reasoning behind multiplying y by another variable in Statement 2 (in this case k)? 2)x^2 -x is a multiple of y let K be the multiple. then x^2-x = K . y Hope this helps
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Re: DS: x multiple of y? [#permalink]
10 Jun 2010, 07:41
so if we have
y^2-y = X
Then we could say with certitude that X is a multiple of Y?
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Re: DS: x multiple of y? [#permalink]
10 Jun 2010, 07:54
Yes. If it was given that y^2-y = x, then x is certainly a multiple of y.
y^2-y = x
y(y-1) = x
y*k = x
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Re: DS: x multiple of y? [#permalink]
17 Jul 2010, 07:52
So from x(x-1)=yk, can we not derive: x=y*k/(x-1)=yk? In which case the answer is C, not A.
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Re: DS: x multiple of y? [#permalink]
17 Jul 2010, 08:12
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dauntingmcgee wrote: So from x(x-1)=yk, can we not derive:
x=y*k/(x-1)=yk?
In which case the answer is C, not A. We don't know whether \frac{k}{x-1} is an integer, hence we can not write x=yn (where n is an integer) from x(x-1)=yk. If x and y are integers great than 1, is x a multiple of y?Is x=ny, where n=integer\geq{1}? (1) 3y^2+7y=x --> y(3y+7)=x --> as 3y+7=integer, then y*integer=x --> x is a multiple of y. Sufficient. (2) x^2-x is a multiple of y --> x^2-x=my --> x(x-1)=my --> x can be multiple of y ( x=2 and y=2) OR x-1 can be multiple of y ( x=3 and y=2) or their product can be multiple of y ( x=3 and y=6). Not sufficient. Answer: A. Hope it helps.
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Re: DS: x multiple of y? [#permalink]
17 Jul 2010, 10:46
Yes, that is great. Thank you. Guess I'm a little rustier than I thought.
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Re: DS: x multiple of y?
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17 Jul 2010, 10:46
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