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# M61-15

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7465
GMAT 1: 760 Q51 V42
GPA: 3.82

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18 Jun 2018, 04:12
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Difficulty:

25% (medium)

Question Stats:

83% (01:07) correct 17% (03:33) wrong based on 6 sessions

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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. $$n^2-m^2$$

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"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" Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7465 GMAT 1: 760 Q51 V42 GPA: 3.82 Re M61-15 [#permalink] ### Show Tags 18 Jun 2018, 04:12 Official Solution: 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. $$n^2-m^2$$ $$x^2-y^2$$ $$= (m^2+n^2)^2 – (2mn)^2$$ $$= m^4 + 2m^2 n^2 + n^4 – 4m^2 n^2$$ $$= m^4 – 2m^2 n^2 + n^4$$ $$= (m^2-n^2)^2$$ Therefore, $$\sqrt{(x^2-y^2 )}$$ $$=\sqrt{(m^2-n^2)^2}$$ $$= |m^2-n^2|$$ $$= m^2-n^2$$, since $$m^2>n^2$$. 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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18 Jun 2018, 04:41
Bunuel wrote:
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. $$n^2-m^2$$

$$X=m^2+n^2.........x^2=(m^2+n^2)^2=m^4+n^4+2(mn)^2=m^4+n^4+2(mn)^2+2(mn)^2-2(mn)^2$$......
$$x^2=m^4+n^4-2(mn)^2+(2mn)^2=(m^2-n^2)^2+y^2........x^2-y^2=(m^2-n^2)^2.......√(x^2-y^2)=m^2-n^2$$

D
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11 Jan 2019, 16:39
Why m^2>n^2?

Can anybody explain?
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22 May 2019, 08:48
Pritam_Pf wrote:
Why m^2>n^2?

Can anybody explain?

m<n<0

That means m and n are negative such as -4 < -2 so m2 > n2
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Re: M61-15   [#permalink] 22 May 2019, 08:48
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# M61-15

Moderators: chetan2u, Bunuel