If xy = z, what is the value of x ? (1) y =2z (2) y2 = 4

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If xy = z, what is the value of x ? (1) y =2z (2) y2 = 4 [#permalink]

26 Dec 2010, 14:28

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If xy = z, what is the value of x ?

(1) y =2z
(2) y2 = 4

[Reveal] Spoiler: OA

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Re: Algebra DS [#permalink]

26 Dec 2010, 15:07

xy = z

1) y = 2z

=> x*2z = z
=> x*2z -z = 0
=> z(x*2 -1)= 0

z=0 or (x*2-1)=0 not sufficient

2)

y2=4
=> y=2
=> x*2=z
=> not sufficient

with 1+2)

y=2z & y=2
=>2z=2
=>z=1

z=1 for z(x*2 -1)= 0
=> 1(x*2-1) = 0
=> 2x-1=0
=> 2x = 1
=> x = 1/2

Sufficient
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Re: Algebra DS [#permalink]

26 Dec 2010, 15:46

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rxs0005 wrote:

If xy = z, what is the value of x ?

(1) y =2z
(2) y2 = 4

I guess it's y^2=4 in statement (2).

If xy = z, what is the value of x ?

(1) y =2z --> 2zx=z --> z(2x-1)=0 --> either z=0 (and x can take any value) or x=\frac{1}{2} (and z can take any value). Not sufficient.
(2) y^2 = 4 --> y=2 or y=-2. Clearly insufficient.

(1)+(2) As y^2=4 and y=2z then it's clear that z\neq{0}, so from (1) must be true that x=\frac{1}{2}. Sufficient.

Answer: C.
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Re: If xy = z, what is the value of x ? (1) y =2z (2) y2 = 4 [#permalink]

02 May 2012, 11:56

Hi for statement 1 after substituting 2Z for Y, I then only got X=1/2. Can you explain why you can't cancel out the two Zs?

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Re: If xy = z, what is the value of x ? (1) y =2z (2) y2 = 4 [#permalink]

02 May 2012, 18:14

shelly22chen wrote:

Hi for statement 1 after substituting 2Z for Y, I then only got X=1/2. Can you explain why you can't cancel out the two Zs?

I am just going to guess and say that you have to account for the possibility that Z = 0. If y = 2*0, when you cancel the Z's as you did above your dividing by zero. So you're left with two answers either x= 1/2 or 0

Re: If xy = z, what is the value of x ? (1) y =2z (2) y2 = 4 [#permalink] 02 May 2012, 18:14

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If xy = z, what is the value of x ? (1) y =2z (2) y2 = 4

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If xy = z, what is the value of x ? (1) y =2z (2) y2 = 4

If xy = z, what is the value of x ? (1) y =2z (2) y2 = 4

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