IMO C.
Separately:
1. X could be smaller or bigger - we dont know.
2. No Y in there, so we cant say anything either.
Together:
Solve the 1st equation for Z = Y^2/X.
Switch in the 2. Z-X>0 to Z > X.
Put the 1st equation into the second --> Z = Y^2/X>X.
--> Y^2>X^2. Therefore we know that Y > X. --> Solution C.
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Inequalities Problem
Source: Beat The GMAT — Data Sufficiency |
Only problem is in option B, Z-X>0 (and not equal to 0)schakiiieee wrote:IMO C.
Separately:
1. X could be smaller or bigger - we dont know.
2. No Y in there, so we cant say anything either.
Together:
Solve the 1st equation for Z = Y^2/X.
Switch in the 2. Z-X=0 to Z = X.
Put the 1st equation into the second --> Z = Y^2/X=X.
--> Y^2=X^2. Therefore we know that Y and X are equal. Y is NOT bigger than X --> Solution C.
Therefore, Z>X and not equal to X
Hmm... true. So did I mess up things or is the answer E?
EDIT: (was a bit confused when i wrote this
)
EDIT: (was a bit confused when i wrote this
)
Last edited by schakiiieee on Thu Oct 09, 2008 7:17 am, edited 1 time in total.
Another way to think about it:gmat009 wrote:If X, Y, and Z are positive integers, is Y>X?
(1) Y^2=XZ
(2) Z-X>0
(1) Y*Y = X*Z
as (2) states that Z>X we know that Y*Y < Z*Z. So X<Y enables Y*Y = X*Z.
x, y, and z are postivie INTEGERS is y >x?
1. Y^2= xz
For example, if y=3, y^2 =9. The only intergers that work for x and z are either 3x3 or 1x9 or 9x1. Therefore Insufficient
2. z-x>0
from this we know z>X but we have no information about Y so Insuffient
From 1+2 we know z is greater than x and to satisfy statement 1 the only values that work is x=1 and z=9. Therefore, Y>X (3>1) suffient
1. Y^2= xz
For example, if y=3, y^2 =9. The only intergers that work for x and z are either 3x3 or 1x9 or 9x1. Therefore Insufficient
2. z-x>0
from this we know z>X but we have no information about Y so Insuffient
From 1+2 we know z is greater than x and to satisfy statement 1 the only values that work is x=1 and z=9. Therefore, Y>X (3>1) suffient
