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If x and y are integers greater than 1, is x a multiple of [#permalink]
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16 Nov 2005, 02:56
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If x and y are integers greater than 1, is x a multiple of y? (1) 3y^2 + 7y = x (2) x^2  x is a multiple of y OPEN DISCUSSION OF THIS QUESTION IS HERE: ifxandyareintegersgreaterthan1isxamultipleofy126736.html
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Re: DS: multiple [#permalink]
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16 Nov 2005, 03:55
themagiccarpet wrote: If x and y are 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) x=3y^2+7y= y ( 3y+7) , since y is an integer> 3y+7 is an integer > x is a multiple of y
>suff
(2) x^2x is a multiple of y
pick number x = 3 ,y =6 > x^2x= 6 is a multiple of 6 but x=3 isn't
x=3, y=3, x^2x= 6 is a multiple of y=3 , x=3 is a multiple of 3
> insuff.



Director
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D
If x and y are integers greater than 1, is x a multiple of y?
(1)3y^2 + 7y = x
x = y(3y+7) hence x is always a multiple as y is an integer so 3y+7 will also be an ingeter . Ans Yes .... Suff
(2)x^2 x is a multiple of y
y=m*(x1)x
as (x1) > 1
and x is also an integer so Y is a multiple of x not the reverse.
No ...suff



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This was in the GMATPrep test I just took. It's A. Why? I have no clue.



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Ok lets see...
X and Y are positiv integers greater than 1
x>1, y>1
(1) can be written as y(3y+1)=x
y.m=x
as we know that y is an integer....3Y+1 is also an integer thus X is a multiple of Y...Sufficient
(2) x(x1)=y
xm=y
hmm this lets see if x=4, y=2...then 4(3)=12...works fine and x is a multiple of Y...if x=5 y=4 then 5(4)=20=which is a multiple of y however x=5 is not a multiple of y=4
A it is



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DS  Prep software divisibility [#permalink]
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30 Jan 2006, 14:03
Hey, please let me see your approaches to this one:
If x and y are integers greater than 1, is x a multiple of y?
1) 3y^2 + 7y = x
2) x^2  x is a multiple of y
Last edited by allabout on 30 Jan 2006, 15:20, edited 1 time in total.



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A
x is a multiple of y means
x = ay where "a" is a +ve integer. (Because x and y are greater than 1)
St1: 3y^2 + 7y = x
i.e x = y(3y+7) ... so a = 3y+7 and will always be a +ve integer. So x is a multiple of y. SUFF
St2: x^2  x... there is no information about y. INSUFF
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Director
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added another infromation, which doesn't affect the result.
Thank you dahiya
I did:
3y^2 + 7y = x
x/y = (3y+7)
which is essentally the same, but I wasn't sure if it's an proper way; of course it is but what made me doubt was
x^2 x is a multiple of y
[x(x1)]/y at first I wasn't sure if I can infer x/y and (x1)/y, now I see clear.



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DS: Multiple [#permalink]
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17 Feb 2006, 13:28
If x and y are 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: Multiple [#permalink]
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17 Feb 2006, 13:41
D.
from i, y (3y+7) = x, (3y+7) is an integer. so it is enough
from ii, x(x1) = yk where k is an integer because x and (x1) both are integer.



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Re: DS: Multiple [#permalink]
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18 Feb 2006, 00:55
Professor wrote: D. from i, y (3y+7) = x, (3y+7) is an integer. so it is enough from ii, x(x1) = yk where k is an integer because x and (x1) both are integer.
briliant explanation))my approach was way too long
agree D it is
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Re: DS: Multiple [#permalink]
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18 Feb 2006, 01:06
Professor wrote: D. from i, y (3y+7) = x, (3y+7) is an integer. so it is enough from ii, x(x1) = yk where k is an integer because x and (x1) both are integer.
A
professor will k/(x1) always be an integer ...?



Director
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k/(x1) will not always be an integer, and that's the point. So X^2  X is a multiple of y does not make necessarily x a multiple of y.
Try x=4 y=3



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agree with D)
to Professor, think that for B) it should be Y=K(X^2X) or Y=KX(X1) and YES X is a multiple of Y



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Agree with (B)
x(x1)/y > either x or (x1) is multiple of y, or both
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allabout wrote: k/(x1) will not always be an integer, and that's the point. So X^2  X is a multiple of y does not make necessarily x a multiple of y.
Try x=4 y=3
stmt1, holds good
but stmt 2 doesnt
tryx=3, then x(x1) = 6 = y
x is not a multiple of y
try x=2, then y=2
x is a multiple of Y
I'm with A



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tryx=3, then x(x1) = 6 = y
x is not a multiple of y
Do you really think that 3 is not a multiple of 6?



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Re: DS: Multiple [#permalink]
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18 Feb 2006, 07:04
gmacvik wrote: If x and y are integers greater than 1, is x a multiple of y?
1) 3y^2 + 7y = X 2) X^2  X is a multiple of y
let me correct myself and change to A.
what i overlooked with (ii) is I assumed (X^2  X) is a multiple of y, which is given. ststement (ii) doesnot tell that x is a multiple of y. if suppose x = 5 and y = 2.
(X^2  X) = yk
255=2k
k=10.
but x=5 is not a multiple of y=2. so ii is not suff.



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Re: DS: Multiple [#permalink]
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19 Feb 2006, 14:26
1) 3y^2 + 7y = X
x=y(3y+7)
professor is right, since 3y+7 is an integer, x is a multiple of y.
2) X^2  X is a multiple of y
x or x1 has to be a multiple of y.
In other words x does not have to be a multiple of y.
Therefore A.
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1)y(3y+7) = x
Sufficient. x is the (3y+7)th multiple of y.
2) x(x1) is a multiple of y. Not sufficient. It could be x being the (x1)th multiple of y or (x1) is the xth multiple of y.
Ans A







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