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Re: If x^2 + y^2 = 29, what is the value of (x - y)^2 ? (1) xy = 10 (2) x [#permalink]
If x^2+y^2=29, what is the value of (x-y)^2?
(1) xy=10
(2) x=5

The OA says the answer is A whereas I think statement 2 is also sufficient as given below.
x=5 hence y^2=29-25=4-->y=+2 or -2. Hence (x-y)^2= (5-2)^2 or (5+2)^2

Is it because of two answer choices, Statement 2 is insufficient?
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Re: If x^2 + y^2 = 29, what is the value of (x - y)^2 ? (1) xy = 10 (2) x [#permalink]
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mtripathy wrote:
If x^2+y^2=29, what is the value of (x-y)^2?
(1) xy=10
(2) x=5

The OA says the answer is A whereas I think statement 2 is also sufficient as given below.
x=5 hence y^2=29-25=4-->y=+2 or -2. Hence (x-y)^2= (5-2)^2 or (5+2)^2

Is it because of two answer choices, Statement 2 is insufficient?

Precisely! When the question is asking for the value of something, then "sufficient" means you can determine a unique individual unambiguous value. There is absolutely only one place on the entire infinity of the number line where that value could be --- that's what "sufficient" means. If you can narrow things down to two values, it's not sufficient. Does that make sense?

Mike :-)
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Re: If x^2 + y^2 = 29, what is the value of (x - y)^2 ? (1) xy = 10 (2) x [#permalink]
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 ? (1) xy = 10 (2) x [#permalink]
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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 ? (1) xy = 10 (2) x [#permalink]
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Since we want the value of \((x-y)^2\), let’s first expand it and write it as \((x-y)^2 = x^2 + y^2 + 2xy\).

We see that the question gives us \(x^2 + y^2\) = 29; so if we are to find the value of \((x-y)^2\), then we need the value of xy.

Statement I alone is sufficient since it gives us the value of xy directly. Note that this is a DS question and you are not expected to plug in the value of xy and \(x^2 + y^2\) into the equation and find out the final value of \((x-y)^2\).

Statement I alone is sufficient to say that we can find the value of \((x-y)^2\). Answer options B, C and E can be eliminated. Possible answer options are A or D.

From statement II alone, x = 5. Now, using this in the equation given as part of the question,\( x^2 + y^2\) = 29, we can say \(y^2\) = 4 or y = 2 or -2.

If x = 5 and y = 2, \((x-y)^2\) = 9; if x = 5 and y = -2, \((x-y)^2\) = 49.

Can we answer the question with a definitive answer? We cannot. Statement II alone is insufficient to find a unique answer to the question. Answer option D can be eliminated.

The correct answer option is A.

Hope that helps!
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Re: If x^2 + y^2 = 29, what is the value of (x - y)^2 ? (1) xy = 10 (2) x [#permalink]
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Jayanth2689 wrote:
If x^2 + y^2 = 29, what is the value of (x - y)^2 ?

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

Solution:

We need to determine the value of (x - y)^2 given that x^2 + y^2 = 29. Notice that (x - y)^2 = x^2 + y^2 - 2xy. Since x^2 + y^2 = 29, then (x - y)^2 = 29 - 2xy. Therefore, if we know the value of xy, then we know the value of (x - y)^2.

Statement One Alone:

Since we know xy = 10, we see that (x - y)^2 = 29 - 2xy = 29 - 2(10) = 9. Statement one alone is sufficient.

Statement Two Alone:

Let’s substitute x = 5 in x^2 + y^2 = 29:

5^2 + y^2 = 29

25 + y^2 = 29

y^2 = 4

y = 2 or -2

If y = 2, then (x - y)^2 = (5 - 2)^2 = 3^2 = 9. If y = -2, then (x - y)^2 = (5 - (-2))^2 = 7^2 = 49. We see that we have two possible values for (x - y)^2. Statement two alone is not sufficient.

Answer: A
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Re: If x^2 + y^2 = 29, what is the value of (x - y)^2 ? (1) xy = 10 (2) x [#permalink]
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