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# If x^2 + y^2 = 29, what is the value of (x - y)^2 ?

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If x^2 + y^2 = 29, what is the value of (x - y)^2 ? [#permalink]

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04 Feb 2014, 01:49
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

If x^2 + y^2 = 29, what is the value of (x - y)^2 ?

(1) xy = 10
(2) x = 5

Data Sufficiency
Question: 73
Category: Algebra Simplifying algebraic expressions
Page: 158
Difficulty: 600

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Re: If x^2 + y^2 = 29, what is the value of (x - y)^2 ? [#permalink]

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04 Feb 2014, 01:50
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SOLUTION

If x^2 + y^2 = 29, what is the value of (x - y)^2 ?

Given: $$x^2+y^2=29$$.
Question: $$(x-y)^2=x^2-2xy+y^2=(x^2+y^2)-2xy=29-2xy=?$$ So, basically we should find the value of $$xy$$

(1) xy = 10. Directly gives us the value we needed. Sufficient.

(2) x = 5. Now even if we substitute the value of $$x$$ in $$x^2+y^2=29$$ we'll get two values for $$y$$: 2 and -2, hence two values for $$(x-y)^2$$: 9 and 49. Not sufficient.

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Re: If x^2 + y^2 = 29, what is the value of (x - y)^2 ? [#permalink]

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04 Feb 2014, 04:46
Ans. A

From S1: we're given the value of x^2+y^2
To find out (x-y)^2=x^2 + y^2 - 2xy we need only xy which is given in S1.Sufficient

From S2;x is given but y is not.So insufficent.
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Re: If x^2 + y^2 = 29, what is the value of (x - y)^2 ? [#permalink]

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04 Feb 2014, 05:13
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x^2 + y^2 = 29. (x-y)^2 = ? or x^2 + y^2 - 2xy = ?
From St1) xy = 10, so x^2 + y^2 - 2xy = 29 - 2*10 = 9 --> Suff
From St2) x = 5. then y = 2 or -2. Results in two values --> not suff

Ans - A
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Re: If x^2 + y^2 = 29, what is the value of (x - y)^2 ? [#permalink]

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05 Feb 2014, 00:33
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(x-y)^2 = x^2 + y^2 - 2xy = 29 - 2xy;

So, we can rephrase the question as "what is the value of xy?" or "what is the value of x & y?"

Statement (1): Sufficient, since we know the value of xy;
Statement (2): Insufficient, since we do not know the value of y;

Ans is (A).
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Re: If x^2 + y^2 = 29, what is the value of (x - y)^2 ? [#permalink]

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08 Feb 2014, 05:33
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SOLUTION

If x^2 + y^2 = 29, what is the value of (x - y)^2 ?

Given: $$x^2+y^2=29$$.
Question: $$(x-y)^2=x^2-2xy+y^2=(x^2+y^2)-2xy=29-2xy=?$$ So, basically we should find the value of $$xy$$

(1) xy = 10. Directly gives us the value we needed. Sufficient.

(2) x = 5. Now even if we substitute the value of $$x$$ in $$x^2+y^2=29$$ we'll get two values for $$y$$: 2 and -2, hence two values for $$(x-y)^2$$: 9 and 49. Not sufficient.

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Re: If x^2 + y^2 = 29, what is the value of (x - y)^2 ? [#permalink]

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12 Mar 2015, 20:05
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Re: If x^2 + y^2 = 29, what is the value of (x - y)^2 ? [#permalink]

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13 Mar 2015, 12:12
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Hi All,

The posters in this thread all seem comfortable with the math involved, so I won't rehash any of that here. Instead, I won't to point out a common-enough design 'element' in DS questions. In many prompts, the question writers are going to test the 'thoroughness' in your thinking. Can you "see" information in more than one way? As such, when dealing with DS questions, you should look for opportunities to "rewrite" information (and sometimes 'rewriting' the question is the "key" to solving it).

Here, we're told that X^2 + Y^2 = 29. That's an interesting piece of information and not something that we would be given all that often. There MUST be a reason why the writer put it there.......

The question asks for the value of (X-Y)^2. This is one of the Classic Quadratics, so it should get you thinking about FOILing. If we just take a moment to FOIL the question, we get....

"What is the value of X^2 -2XY + Y^2?"

NOW the purpose of that original piece of information is clear....it's part of the solution to the question. If we can figure out the value of XY, then we'll have the answer to the question. From here, the rest of the math is pretty straight-forward.

Remember to look for these pattern-based shortcuts. They will appear repeatedly and while they take a little bit of extra work, doing THAT work will make solving the problem that much easier.

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# Special Offer: Save $75 + GMAT Club Tests 60-point improvement guarantee www.empowergmat.com/ ***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*********************** Manager Joined: 01 Aug 2014 Posts: 59 Schools: Rotman '17 (A) GMAT 1: 710 Q44 V42 Followers: 1 Kudos [?]: 5 [0], given: 34 Re: If x^2 + y^2 = 29, what is the value of (x - y)^2 ? [#permalink] ### Show Tags 08 Feb 2016, 23:53 If x^2 + y^2=29, and according to stmt II x=5, then why can we not derive from that that y=2 and xy=10? EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 6701 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: 340 Q170 V170 Followers: 289 Kudos [?]: 1973 [1] , given: 161 Re: If x^2 + y^2 = 29, what is the value of (x - y)^2 ? [#permalink] ### Show Tags 09 Feb 2016, 00:06 1 This post received KUDOS Expert's post Hi Anonamy, If you plug X=5 into X^2 + Y^2=29, then what does that tell you about the value of Y. Be sure to be THOROUGH here. Is Y positive or negative? How would that impact the answer to the given question? Without too much work, you should be able to PROVE that there is more than one answer to the given question when X=5. GMAT assassins aren't born, they're made, Rich _________________ # Rich Cohen Co-Founder & GMAT Assassin # Special Offer: Save$75 + GMAT Club Tests

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Re: If x^2 + y^2 = 29, what is the value of (x - y)^2 ? [#permalink]

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09 Feb 2016, 00:07
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Anonamy wrote:
If x^2 + y^2=29, and according to stmt II x=5, then why can we not derive from that that y=2 and xy=10?

hi,
when you substitute x as 5..
5^2+y^2=29 ..
or y^2=4..
we are not given anything about sign of y, so y can be 2 and -2..
in both cases you will have two different answers..
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Re: If x^2 + y^2 = 29, what is the value of (x - y)^2 ?   [#permalink] 09 Feb 2016, 00:07
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