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# If √x+√y=7 and √x-√y=5, what is the value of xy?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 7230
GMAT 1: 760 Q51 V42
GPA: 3.82
If √x+√y=7 and √x-√y=5, what is the value of xy?  [#permalink]

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14 Mar 2019, 01:56
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Difficulty:

15% (low)

Question Stats:

82% (01:20) correct 18% (02:28) wrong based on 33 sessions

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[GMAT math practice question]

If $$√x+√y=7$$ and $$√x-√y=5$$, what is the value of $$xy$$?

$$A. 16$$
$$B. 25$$
$$C. 36$$
$$D. 49$$
$$E. 64$$

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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" Manager Joined: 21 Feb 2019 Posts: 103 Location: Italy Re: If √x+√y=7 and √x-√y=5, what is the value of xy? [#permalink] ### Show Tags 14 Mar 2019, 02:20 It's given the system of two linear equations: $$\sqrt{x} + \sqrt{y} = 7$$ $$\sqrt{x} - \sqrt{y} = 5$$ Subtraction method gives: $$2\sqrt{y} = 2$$ Hence, $$y = 1$$ Substitute the variable into one of the two linear equations to state the value of $$x$$. If we take the first one, $$\sqrt{x} + 1 = 7$$ $$x = 36$$ As a result, $$xy = 36$$ _________________ If you like my post, Kudos are appreciated! Thank you. MEMENTO AUDERE SEMPER Manager Joined: 05 Oct 2017 Posts: 79 Location: India Concentration: Finance, International Business Schools: ISB '21, IIMA , IIMB GPA: 4 WE: Analyst (Energy and Utilities) Re: If √x+√y=7 and √x-√y=5, what is the value of xy? [#permalink] ### Show Tags 14 Mar 2019, 02:22 √x+√y=7...i) and √x-√y=5...ii) Adding i) & ii), we get 2√x=12 => √x = 6 => x = 36 Substituting the value in i) we get, √y = 1 => y = 1 So xy = 36 Option C) is the answer VP Joined: 31 Oct 2013 Posts: 1322 Concentration: Accounting, Finance GPA: 3.68 WE: Analyst (Accounting) Re: If √x+√y=7 and √x-√y=5, what is the value of xy? [#permalink] ### Show Tags 14 Mar 2019, 02:57 MathRevolution wrote: [GMAT math practice question] If $$√x+√y=7$$ and $$√x-√y=5$$, what is the value of $$xy$$? $$A. 16$$ $$B. 25$$ $$C. 36$$ $$D. 49$$ $$E. 64$$ Given, $$√x+√y=7$$ $$√x-√y=5$$ ...........................................Adding both equation . 2√x = 12 √x = 6 Substitute the value of √x into equation 1. 6 + √y = 7 √y = 1 Now are looking for the value of xy. √x√y = 6*1 $$\sqrt{xy}$$ = 6 xy = 36. C is the correct answer. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7230 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If √x+√y=7 and √x-√y=5, what is the value of xy? [#permalink] ### Show Tags 17 Mar 2019, 18:18 => Adding the two equations yields $$2√x = 12$$, so $$x = 36.$$ Subtracting the two equations yields $$2√y = 2$$, so $$y = 1$$. Therefore, $$xy = 36$$. Therefore, the answer is C. Answer: C _________________ 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"
Re: If √x+√y=7 and √x-√y=5, what is the value of xy?   [#permalink] 17 Mar 2019, 18:18
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