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# If x and y are positive, what's the value of x? 1. 200% of x

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SVP
Joined: 05 Jul 2006
Posts: 1747
If x and y are positive, what's the value of x? 1. 200% of x [#permalink]

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10 Aug 2009, 11:02
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If x and y are positive, what's the value of x?

1. 200% of x = 400% of y
2. xy is the square of a positive integer
Director
Joined: 01 Apr 2008
Posts: 881
Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014

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10 Aug 2009, 11:20
yezz wrote:
If x and y are positive, what's the value of x?

1. 200% of x = 400% of y
2. xy is the square of a positive integer

I get E.

1) we don't have value of y,so insufficient.
2) xy can be 1,4,9,...
combining,
x/y = 2, now if x is a fraction y is also a fraction, in that case xy would not be a square of a positive integer, so x and y are integers.
I could not find any combination where x/y = 2 and xy is a square of a positive integer.

OA and OE pls
SVP
Joined: 05 Jul 2006
Posts: 1747

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10 Aug 2009, 11:24
Economist wrote:
yezz wrote:
If x and y are positive, what's the value of x?

1. 200% of x = 400% of y
2. xy is the square of a positive integer

I get E.

1) we don't have value of y,so insufficient.
2) xy can be 1,4,9,...
combining,
x/y = 2, now if x is a fraction y is also a fraction, in that case xy would not be a square of a positive integer, so x and y are integers.
I could not find any combination where x/y = 2 and xy is a square of a positive integer.

OA and OE pls

will do after some discussion..ok
Intern
Joined: 29 Jun 2009
Posts: 15
Location: Dallas TX

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10 Aug 2009, 12:07
E

I don't think there is any combination where x = 2y and xy is a perfect square.

xy = z^2
2y^2 = z^2
z = y . Sqrt2

and both z and y are integers. I don't know if there is any
Senior Manager
Joined: 20 Mar 2008
Posts: 452

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10 Aug 2009, 12:12
St. 1 : No values for x or y. So Insuff.

St. 2: XY can have multiple values. Insuff.

Combined: We know from St. 1, x = 2y, hence xy = 2y.y = 2y^2.

Now, if y = 2^-.5, then 2y^2 = 2. 1 / (2^.5)^2 = 1. (x & y can be fractions, but not xy.)

1 is a square of a positive integer, 1.

For no other value of y will this hold true. Hence, sufficient.

So, C for me.
Director
Joined: 01 Apr 2008
Posts: 881
Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014

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10 Aug 2009, 12:20
Good one Jivana. So finally we got a possibility Thanks!
C.
SVP
Joined: 05 Jul 2006
Posts: 1747

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10 Aug 2009, 12:34
Econ... u wr right ....E

St1: x = 2y Infinite possibilities: INSUFF

St2: xy is a perfect square. Infinite possibilities: INSUFF

Together:
xy = 2x^2

2x^2 is a perfect square.
x = √8, y = 2* √8
x = √18 y = 2*√18
Infinitie possibilities: INSUFF
Director
Joined: 01 Apr 2008
Posts: 881
Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014

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10 Aug 2009, 22:28
arghhhhhhh !!! Thanks for the clarification yezz
Re: percents   [#permalink] 10 Aug 2009, 22:28
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