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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## If x^2+y^2=28 and xy=11, what is the value of (x+y)^2? tagged by: Max@Math Revolution ##### This topic has 4 expert replies and 0 member replies ### GMAT/MBA Expert ## If x^2+y^2=28 and xy=11, what is the value of (x+y)^2? ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult [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 _________________ Math Revolution Finish GMAT Quant Section with 10 minutes to spare. The one-and-only Worldâ€™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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Max@Math Revolution 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
$$? = {\left( {x + y} \right)^2}$$
$$\left\{ \matrix{ {x^2} + {y^2} = 28 \hfill \cr 2xy = 2 \cdot 11 \hfill \cr} \right.\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( + \right)} \,\,\,\,\,\,? = 28 + 2 \cdot 11 = 50$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

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Max@Math Revolution 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
Every test-taker should know the following quadratic identities:
(x+y)Â² = xÂ² + yÂ² + 2xy
(x-y)Â² = xÂ² + yÂ² - 2xy
(x+y)(x-y)Â² = xÂ² - yÂ²

Substituting xÂ²+yÂ²=28 and xy=11 into (x+y)Â² = xÂ² + yÂ² + 2xy, we get:
(x+y)Â² = 28 + 2*11 = 50.

An alternate approach is to BALLPARK.
x and y must have a product of 11, while xÂ²+yÂ² = 28.
If x=3 and y=4, then xy=12 and xÂ²+yÂ² = 3Â²+4Â² = 25.
The values in blue are reasonably close to the values in red.
If x=3 and y=4, then (x+y)Â² = (3+4)Â² = 49.
Thus, the correct answer must be close to 49.
Only C is viable.

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(x+y)^2 = x^2 + 2xy + y^2 = x^2 + y^2 + 2xy = 28 + 2*11 = 28 + 22 = 50.

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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 Email to : info@mathrevolution.com ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2852 messages Followed by: 18 members Upvotes: 43 Max@Math Revolution 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 Answer: C _________________ Scott Woodbury-Stewart Founder and CEO scott@targettestprep.com See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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