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# If m<n<0, x=m^2+n^2, and y=2mn, what is the va

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6815
GMAT 1: 760 Q51 V42
GPA: 3.82
If m<n<0, x=m^2+n^2, and y=2mn, what is the va  [#permalink]

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30 Jan 2018, 02:15
1
2
00:00

Difficulty:

45% (medium)

Question Stats:

71% (02:07) correct 29% (02:25) wrong based on 77 sessions

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[GMAT math practice question]

If $$m<n<0$$, $$x=m^2+n^2$$, and $$y=2mn$$, what is the value of $$\sqrt{x^2-y^2}$$, in terms of $$m$$ and $$n$$?

$$A. m^2+n^2$$
$$B. 2m^2+n^2$$
$$C. m^2+2n^2$$
$$D. m^2-n^2$$
$$E. n^2-m^2$$

_________________

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 $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Senior Manager Joined: 17 Oct 2016 Posts: 318 Location: India Concentration: Operations, Strategy GPA: 3.73 WE: Design (Real Estate) Re: If m<n<0, x=m^2+n^2, and y=2mn, what is the va [#permalink] ### Show Tags 30 Jan 2018, 02:46 2 D x=m²+n², y=2mn Now rt($$x²-y²$$) =rt($$(x+y)(x-y)$$) =rt($$(m²+n²+2mn)(m²+n²-2mn)$$) =rt($$(m+n)²(m-n)²$$) =(m+n)(m-n) =m²-n² _________________ Help with kudos if u found the post useful. Thanks Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6815 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If m<n<0, x=m^2+n^2, and y=2mn, what is the va [#permalink] ### Show Tags 01 Feb 2018, 00:35 => $$x^2-y^2$$ $$= (m^2+n^2)^2 – (2mn)^2$$ $$= (m^2+n^2)^2 – 4m^2n^2$$ $$= m^4 + 2m^2n^2 + n^4 – 4m^2n^2$$ $$= m^4 – 2m^2n^2 + n^4$$ $$= (m^2-n^2)^2$$ Therefore, $$\sqrt{x^2-y^2}$$ $$=\sqrt{(m^2-n^2)^2}$$ $$= |m^2-n^2|$$ $$= m^2-n^2$$, since $$m^2 > n^2$$. Therefore, the answer is D. Answer: D _________________ 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$149 for 3 month Online Course"
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Re: If m<n<0, x=m^2+n^2, and y=2mn, what is the va  [#permalink]

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03 Feb 2018, 11:27
1
This is a good, tricky question. If you forget that m and n are negative numbers (based on the given m<n<0) and assign them numbers to work the problem out (in my case, m=2 and n=3), E will work out to be the correct answer.

This just reinforces that you need to remember ALL given prompts. It's not enough to just write them down - I did and still fell into the trap. When testing scenarios, you need to really be sure you are staying in the confines of all the given prompts.
Re: If m<n<0, x=m^2+n^2, and y=2mn, what is the va &nbs [#permalink] 03 Feb 2018, 11:27
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