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# If √x -√y+√z=0, which of the following is true?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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If √x -√y+√z=0, which of the following is true?  [#permalink]

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28 Mar 2016, 22:43
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Difficulty:

85% (hard)

Question Stats:

54% (02:37) correct 46% (02:23) wrong based on 222 sessions

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If $$√x -√y+√z=$$0, which of the following is true?

A. $$x^2+y^2+z^2=xy+xz+yz$$

B. $$x^2+y^2+z^2=2xy+2xz+2yz$$

C. $$x^2+y^2-z^2=2xy+2xz-2yz$$

D. $$x^2-y^2-z^2=xy+xz+yz$$

E. $$x^4+y^4+z^4=2xy+2xz+2yz$$

* A solution will be posted in two days.

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" SC Moderator Joined: 13 Apr 2015 Posts: 1694 Location: India Concentration: Strategy, General Management GMAT 1: 200 Q1 V1 GPA: 4 WE: Analyst (Retail) Re: If √x -√y+√z=0, which of the following is true? [#permalink] ### Show Tags 29 Mar 2016, 00:51 1 MathRevolution wrote: If √x -√y+√z=0, which of the following is true? A. x^2+y^2+z^2=xy+xz+yz B. x^2+y^2+z^2=2xy+2xz+2yz C. x^2+y^2-z^2=2xy+2xz-2yz D. x^2-y^2-z^2=xy+xz+yz E. x^4+y^4+z^4=2xy+2xz+2yz $$\sqrt{x} + \sqrt{z} = \sqrt{y}$$ $$x + z + 2\sqrt{xz} = y$$ $$x + z - y = -2\sqrt{xz}$$ $$(a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca$$ $$x^2 + z^2 + y^2 + 2xz - 2yz - 2xy = 4xz$$ $$x^2 + y^2 + z^2 = 2xy + 2yz + 2xz$$ Answer: B Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6369 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If √x -√y+√z=0, which of the following is true? [#permalink] ### Show Tags 30 Mar 2016, 23:21 If √x -√y+√z=0, which of the following is true? A. x^2+y^2+z^2=xy+xz+yz B. x^2+y^2+z^2=2xy+2xz+2yz C. x^2+y^2-z^2=2xy+2xz-2yz D. x^2-y^2-z^2=xy+xz+yz E. x^4+y^4+z^4=2xy+2xz+2yz If you square the both equations, they become x+z+2√xz=y, x+z-y=-2√xz. If you once again square the both equations, x^2+z^2+y^2+2zx-2xy-2zy=4xz is derived and eventually becomes x^2+y^2+z^2=2xy+2yz+2zx. Thus, the answer is B. _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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Re: If √x -√y+√z=0, which of the following is true?  [#permalink]

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25 Dec 2017, 05:49
1
1
MathRevolution wrote:
If √x -√y+√z=0, which of the following is true?

A. x^2+y^2+z^2=xy+xz+yz
B. x^2+y^2+z^2=2xy+2xz+2yz
C. x^2+y^2-z^2=2xy+2xz-2yz
D. x^2-y^2-z^2=xy+xz+yz
E. x^4+y^4+z^4=2xy+2xz+2yz

* A solution will be posted in two days.

In case one does not remembers the formula, plugging smart numbers will be highly effective.

Let $$x=z=1$$ & $$y=4$$. this satisfies our stem equation. Test the values in the options and the option where $$LHS=RHS$$ will be correct

For Option B $$LHS=1^2+4^2+1^2=18$$

$$RHS=2*1*4+2*1*1+2*4*1=18$$.

For other options, LHS will not be equal to RHS
Intern
Joined: 16 Dec 2017
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Re: If √x -√y+√z=0, which of the following is true?  [#permalink]

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27 Dec 2017, 09:51
MathRevolution wrote:
If √x -√y+√z=0, which of the following is true?

A. x^2+y^2+z^2=xy+xz+yz
B. x^2+y^2+z^2=2xy+2xz+2yz
C. x^2+y^2-z^2=2xy+2xz-2yz
D. x^2-y^2-z^2=xy+xz+yz
E. x^4+y^4+z^4=2xy+2xz+2yz

If you square the both equations, they become x+z+2√xz=y, x+z-y=-2√xz. If you once again square the both equations, x^2+z^2+y^2+2zx-2xy-2zy=4xz is derived and eventually becomes x^2+y^2+z^2=2xy+2yz+2zx.

Thank you. Could you help me understand where the highlighted portion came from?
PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1218
Location: India
GPA: 3.82
If √x -√y+√z=0, which of the following is true?  [#permalink]

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27 Dec 2017, 09:56
rb60006 wrote:
MathRevolution wrote:
If √x -√y+√z=0, which of the following is true?

A. x^2+y^2+z^2=xy+xz+yz
B. x^2+y^2+z^2=2xy+2xz+2yz
C. x^2+y^2-z^2=2xy+2xz-2yz
D. x^2-y^2-z^2=xy+xz+yz
E. x^4+y^4+z^4=2xy+2xz+2yz

If you square the both equations, they become x+z+2√xz=y, x+z-y=-2√xz. If you once again square the both equations, x^2+z^2+y^2+2zx-2xy-2zy=4xz is derived and eventually becomes x^2+y^2+z^2=2xy+2yz+2zx.

Thank you. Could you help me understand where the highlighted portion came from?

Hi rb60006

we can rearrange the equation and write $$\sqrt{x}+\sqrt{z}=\sqrt{y}$$, so on squaring it will be of the form $$(a+b)^2=a^2+b^2+2ab$$
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Joined: 20 Oct 2017
Posts: 26
Re: If √x -√y+√z=0, which of the following is true?  [#permalink]

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09 Jan 2018, 08:31
Is this a 700 level question?
PS Forum Moderator
Joined: 25 Feb 2013
Posts: 1218
Location: India
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Re: If √x -√y+√z=0, which of the following is true?  [#permalink]

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09 Jan 2018, 08:37
kritikalal wrote:
Is this a 700 level question?

Hi kritikalal

Check the "Tag" section just above the question. you will get all the details
Re: If √x -√y+√z=0, which of the following is true? &nbs [#permalink] 09 Jan 2018, 08:37
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