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# If x and y are integers greater than 1, is x a multiple of

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Director
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If x and y are integers greater than 1, is x a multiple of [#permalink]  22 Jul 2007, 20:18
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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.

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Re: DS - number properties [#permalink]  22 Jul 2007, 20:38
asaf 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.

A for me.

stmt 1: y*(3y+7) = x
or, 3y+7 = x/y
Since, 3y+7 must be an integer, so too must be x/y. Hence, x is a multiple of y. sufficient.

stmt 2: x*(x-1) = ky (k is some integer greater than 0)
This is not sufficient. e.g. x=3 and y=2; x=4 and y=2
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I think E.

I cant share my solution because I couldn't solve this easily. 1 and 2 alone look insufficient. So I made an educated guess.
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St1:
y(3y+7) = x
3y+7 = x/y
Since 3y + 7 must be integer, then x/y must be integer and x must be a multiple of y if x/y = integer.

St2:
x(x-1) = ym
(x/y)(x-1) = m
Since m is an integer, (x-1) is an integer then x/y must be an integer for the relationship to hold. So x must be a multiple of y.

Ans D
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ywilfred wrote:
St1:
y(3y+7) = x
3y+7 = x/y
Since 3y + 7 must be integer, then x/y must be integer and x must be a multiple of y if x/y = integer.

St2:
x(x-1) = ym
(x/y)(x-1) = m
Since m is an integer, (x-1) is an integer then x/y must be an integer for the relationship to hold. So x must be a multiple of y.

Ans D

I do not think statement 2 can be sufficient. (x-1) and not x may be a multiple of y.
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sumande wrote:
ywilfred wrote:
St1:
y(3y+7) = x
3y+7 = x/y
Since 3y + 7 must be integer, then x/y must be integer and x must be a multiple of y if x/y = integer.

St2:
x(x-1) = ym
(x/y)(x-1) = m
Since m is an integer, (x-1) is an integer then x/y must be an integer for the relationship to hold. So x must be a multiple of y.

Ans D

I do not think statement 2 can be sufficient. (x-1) and not x may be a multiple of y.

yeah.. missed that point. Ouch!
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Re: DS - number properties [#permalink]  23 Jul 2007, 07:27
asaf 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.

I am going with B .

1. y(3y +7 ) = x . I think it means y is a multiple of x and not as it is asked "is x a multiple of h?" So insufficient.

2. x(x-2) = ky . This proves x is a multiple of y .Sufficient

So B .

BTW , whats the OA ?
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Re: DS - number properties [#permalink]  23 Jul 2007, 07:46
ashkrs wrote:
asaf 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.

I am going with B .

1. y(3y +7 ) = x . I think it means y is a multiple of x and not as it is asked "is x a multiple of h?" So insufficient.

2. x(x-2) = ky . This proves x is a multiple of y .Sufficient

So B .

BTW , whats the OA ?

The question clearly asks if "x is a multiple of y" !!
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Re: DS - number properties [#permalink]  24 Jul 2007, 07:19
sumande wrote:
ashkrs wrote:
asaf 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.

I am going with B .

1. y(3y +7 ) = x . I think it means y is a multiple of x and not as it is asked "is x a multiple of h?" So insufficient.

2. x(x-2) = ky . This proves x is a multiple of y .Sufficient

So B .

BTW , whats the OA ?

The question clearly asks if "x is a multiple of y" !!

I think I am getting my terminology wrong. Please correct me .

If X is a multiple of Y .
I understand that as : if Y = 36 then X can be 1 2 3 4 6 12 18.
Intern
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Clear A.
x= y(3y+7) meaning x is a multiple of y.
Intern
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y*(3y+7)=x sufficient

x(x-1)= y ; this would mean that y is a multiple of x. it is not the question?

Senior Manager
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I say A

statment in A can be factorized into
y(3y+7)=x
3y+7 must be an integer as y >1 and int

B

x(x-1)=ky

where k is int

therefore, x = (k/x-1)y

k/x-1 need not be an integer

say if x =18, x-1 = 17 and k =5 then x is not a multiple of y
Hence INSIFF
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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.

OK lets see...

x/y=N where N is an integer?

1) Y(3Y+7)=x; x/y= (3Y+7) we are told x and y are integers...therefor RHS is an integer...which inturn means RHS is an integer...therefore X is a multiple..sufficient..

2) x(x-1)=y/N ...we dont know if X or X-1 is the multiple of Y..therefore insufficient...

A it is..
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Re: DS - number properties [#permalink]  25 Jul 2007, 08:57
asaf 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

A too...........

from 1: 3y^2 + 7y = x
y (3y + 7) = x
in this case, 3y+7 is an integer. so x is a multiple of x.

from 2: x^2 - x = yk
x (x -1) = yk
x (x -1) = yk
k could be or could not be x or x-1. suppose, x = 4, x-1=3, k =1 and y = 12. in this case x is not a multiple of y. if x = 4, x-1 = 3, y = 3 and k =4, x is a multiple of y.
Re: DS - number properties   [#permalink] 25 Jul 2007, 08:57
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