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• ### $450 Tuition Credit & Official CAT Packs FREE November 15, 2018 November 15, 2018 10:00 PM MST 11:00 PM MST EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) # If xy = z, what is the value of x ? (1) y =2z (2) y2 = 4  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Director Joined: 07 Jun 2004 Posts: 600 Location: PA If xy = z, what is the value of x ? (1) y =2z (2) y2 = 4 [#permalink] ### Show Tags 26 Dec 2010, 13:28 2 6 00:00 Difficulty: 85% (hard) Question Stats: 38% (01:36) correct 62% (01:14) wrong based on 211 sessions ### HideShow timer Statistics If xy = z, what is the value of x ? (1) y =2z (2) y2 = 4 _________________ If the Q jogged your mind do Kudos me : ) Manager Joined: 20 Dec 2010 Posts: 156 Location: Stockholm, Sweden Re: Algebra DS [#permalink] ### Show Tags 26 Dec 2010, 14:07 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 _________________ 12/2010 GMATPrep 1 620 (Q34/V41) 01/2011 GMATPrep 2 640 (Q42/V36) 01/2011 GMATPrep 3 700 (Q47/V39) 02/2011 GMATPrep 4 710 (Q48/V39) 02/2011 MGMAT CAT 1 650 (Q46/V32) 02/2011 MGMAT CAT 2 680 (Q46/V36) 02/2011 MGMAT CAT 3 710 (Q45/V41) Math Expert Joined: 02 Sep 2009 Posts: 50544 If xy = z, what is the value of x ? (1) y =2z (2) y2 = 4 [#permalink] ### Show Tags 26 Dec 2010, 14:46 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. Answer: C. _________________ Intern Joined: 10 Jan 2012 Posts: 1 Re: If xy = z, what is the value of x ? (1) y =2z (2) y2 = 4 [#permalink] ### Show Tags 02 May 2012, 10:56 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? Intern Joined: 05 Mar 2012 Posts: 5 Re: If xy = z, what is the value of x ? (1) y =2z (2) y2 = 4 [#permalink] ### Show Tags 02 May 2012, 17:14 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 EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 12841 Location: United States (CA) 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] ### Show Tags 08 Feb 2015, 17:50 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 _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Intern
Joined: 16 Dec 2017
Posts: 5
Re: If xy = z, what is the value of x ? (1) y =2z (2) y2 = 4  [#permalink]

### Show Tags

01 Apr 2018, 14:22
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?
Math Expert
Joined: 02 Sep 2009
Posts: 50544
Re: If xy = z, what is the value of x ? (1) y =2z (2) y2 = 4  [#permalink]

### Show Tags

01 Apr 2018, 20:03
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.
_________________
Re: If xy = z, what is the value of x ? (1) y =2z (2) y2 = 4 &nbs [#permalink] 01 Apr 2018, 20:03
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