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# If x^2+y^2=28 and xy=11, what is the value of (x+y)^2?

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Math Revolution GMAT Instructor
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If x^2+y^2=28 and xy=11, what is the value of (x+y)^2?  [#permalink]

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25 Dec 2018, 02:08
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86% (01:01) correct 14% (01:50) wrong based on 49 sessions

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[Math Revolution GMAT math practice question]

If $$x^2+y^2=28$$ and $$xy=11$$, what is the value of $$(x+y)^2$$?

$$A. 28$$
$$B. 39$$
$$C. 50$$
$$D. 61$$
$$E. 72$$

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" VP Joined: 31 Oct 2013 Posts: 1392 Concentration: Accounting, Finance GPA: 3.68 WE: Analyst (Accounting) Re: If x^2+y^2=28 and xy=11, what is the value of (x+y)^2? [#permalink] ### Show Tags 25 Dec 2018, 06:46 1 MathRevolution wrote: [Math Revolution GMAT math practice question] If $$x^2+y^2=28$$ and $$xy=11$$, what is the value of $$(x+y)^2$$? $$A. 28$$ $$B. 39$$ $$C. 50$$ $$D. 61$$ $$E. 72$$ $$( x + y)^2$$ =$$x^2 + 2xy + y^2$$ = 28 + 2.11 = 50. C is the answer. LBS Moderator Joined: 04 Jun 2018 Posts: 587 Location: Germany Concentration: General Management, Finance GMAT 1: 730 Q47 V44 GPA: 3.4 WE: Analyst (Transportation) Re: If x^2+y^2=28 and xy=11, what is the value of (x+y)^2? [#permalink] ### Show Tags 25 Dec 2018, 07:08 If we expand (x+y)² we end up at x² + 2xy + y² (Bionomical Theorem) Notice that we were already provided with the solutions to the respective parts of the equation: x² + y² = 28 xy = 11 Thus, we can plug those values into our equation: 28 + 2(11) = 50 _________________ Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7590 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If x^2+y^2=28 and xy=11, what is the value of (x+y)^2? [#permalink] ### Show Tags 27 Dec 2018, 02:18 => $$(x+y)^2 = x^2 + 2xy + y^2 = x^2 + y^2 + 2xy = 28 + 2*11 = 28 + 22 = 50.$$ 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$79 for 1 month Online Course"
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Re: If x^2+y^2=28 and xy=11, what is the value of (x+y)^2?  [#permalink]

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27 Dec 2018, 11:04
(x+y)^2 = x^2+ y^2 + 2xy
substitute the values
28+22= 50 (C)
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Re: If x^2+y^2=28 and xy=11, what is the value of (x+y)^2?  [#permalink]

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04 Feb 2019, 18:41
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If $$x^2+y^2=28$$ and $$xy=11$$, what is the value of $$(x+y)^2$$?

$$A. 28$$
$$B. 39$$
$$C. 50$$
$$D. 61$$
$$E. 72$$

If we expand the expression (x + y)^2, we obtain x^2 + y^2 + 2xy. We can now evaluate the new expression by substituting the given values :

28 + 2 x 11 = 28 + 22 = 50

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Re: If x^2+y^2=28 and xy=11, what is the value of (x+y)^2?   [#permalink] 04 Feb 2019, 18:41
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