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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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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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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.

Answer: 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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New post 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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New post 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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New post 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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New post 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.

Answer: A.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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

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

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

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

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New post 09 Feb 2016, 00:06
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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.

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

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New post 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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