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

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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
Manager  Joined: 20 Dec 2010
Posts: 144
Location: Stockholm, Sweden
Re: Algebra DS  [#permalink]

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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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Joined: 02 Sep 2009
Posts: 58453
If xy = z, what is the value of x ? (1) y =2z (2) y2 = 4  [#permalink]

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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.

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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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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?
Intern  Joined: 05 Mar 2012
Posts: 5
Re: If xy = z, what is the value of x ? (1) y =2z (2) y2 = 4  [#permalink]

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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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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If xy = z, what is the value of x ? (1) y =2z (2) y2 = 4  [#permalink]

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

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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?
Math Expert V
Joined: 02 Sep 2009
Posts: 58453
Re: If xy = z, what is the value of x ? (1) y =2z (2) y2 = 4  [#permalink]

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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.
_________________ 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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