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

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Director
Joined: 07 Jun 2004
Posts: 555
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If xy = z, what is the value of x ? (1) y =2z (2) y2 = 4  [#permalink]

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26 Dec 2010, 14:28
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Difficulty:

85% (hard)

Question Stats:

38% (01:36) correct 62% (01:15) wrong based on 222 sessions

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

(1) y =2z
(2) y2 = 4
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Joined: 20 Dec 2010
Posts: 144
Location: Stockholm, Sweden

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

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26 Dec 2010, 15:46
1
1
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.

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

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02 May 2012, 11:56
1
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]

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

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08 Feb 2015, 18:50
1
Hi All,

Both Mackieman and Bunuel have provided solutions that are spot-on, so I won't rehash any of that here. Instead I want to focus on the brief discussion in the last two posts in this thread - since the subject involves a math "issue" that you WILL see on Test Day.

When it comes to "canceling out" variables, adding or subtracting is just fine (and you should take advantage of those rules to simplify your work).

For example:
X + Y = 2X
Y = 2X - X
Y = X

However, you have to be VERY CAREFUL about multiplying or dividing variables away....you might end up accidentally eliminating some of the correct answers....

For example:
N^2 = N

This equation has 2 solutions: N = 0 and N = 1.
If you decide to "divide out" the Ns, then look at what happens...

N^2 = N
(N^2)/N = (N)/N
N = 1

You've now "LOST" one of the original solutions (where's N = 0 in this equation?).

Be on the lookout for this issue, since you'll see it at least once on Test Day (look for it in DS questions).

GMAT assassins aren't born, they're made,
Rich
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Posts: 7
Re: If xy = z, what is the value of x ? (1) y =2z (2) y2 = 4  [#permalink]

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01 Apr 2018, 15:22
Bunuel wrote:
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.

Buniel,

Can you please provide an explanation why z won't be negative given statements 1 and 2? Why can't we assume z=-1?
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Posts: 58453
Re: If xy = z, what is the value of x ? (1) y =2z (2) y2 = 4  [#permalink]

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01 Apr 2018, 21:03
1
futurephilantropist wrote:
Bunuel wrote:
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.

Buniel,

Can you please provide an explanation why z won't be negative given statements 1 and 2? Why can't we assume z=-1?

$$z\neq{0}$$ means that z is not 0, not that z is not negative. z is not 0 because we got that y = 2z and y = 2 or y = -2, thus z = 1 or z = -1.
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Re: If xy = z, what is the value of x ? (1) y =2z (2) y2 = 4   [#permalink] 01 Apr 2018, 21:03
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