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If x^2 + y^2 = 29, what is the value of (x-y)^2 (1) xy = 10

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

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New post 23 Jul 2014, 03:01
Kconfused wrote:
Bunuel wrote:
krit wrote:
If x^2 + y^2 = 29, what is the value of (x-y)^2

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

Hi guys, I'd like some help here. The answer is A. I see why (1) is sufficient, but I don't get why (2) is not. We can just simply plug x = 5 into the equation, find y, and then solve for (x-y)^2

Thanks


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.

Hope it's clear.


And I thought we consider only the positive value of a square root!!!
Not so?


When the GMAT provides the square root sign for an even root, such as \(\sqrt{x}\) or \(\sqrt[4]{x}\), then the only accepted answer is the positive root. That is, \(\sqrt{4}=2\), NOT +2 or -2.

In contrast, the equation \(x^2=4\) has TWO solutions, +2 and -2.

Hope it's clear.
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Re: If x^2 + y^2 = 29, what is the value of (x-y)^2 (1) xy = 10 [#permalink]

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New post 19 Sep 2016, 07:09
A is correct. Here's why:

(1) xy = 10 --> From this we know 2x5 could work or 10x1/2, but since x^2 + y^2 = 29 we know the second alternative can be eliminated. Thus we are left with +/- 2 and +/- 5.

If you plug either (both positive or both negative) into (x+y)^2, you will get the same answer.

SUFFICIENT

(2) x = 5

Plug into original equation --> 25 + y^2 = 29 --> y^2 = 4 --> y = +/- 2

NOT SUFFICIENT

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

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New post 11 Oct 2017, 07:28
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If|x+y=15,x-y=24,solve(1)/(4)x^2-4y^2
I thank the people who are willing to teach me.

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

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New post 11 Oct 2017, 07:35
Christine Christina wrote:
If|x+y=15,x-y=24,solve(1)/(4)x^2-4y^2
I thank the people who are willing to teach me.

Posted from my mobile device


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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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Kudos [?]: 135172 [0], given: 12667

Re: If x^2 + y^2 = 29, what is the value of (x-y)^2 (1) xy = 10   [#permalink] 11 Oct 2017, 07:35

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