GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 17 Jul 2018, 00:41

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 47032
Re: If x^2 + y^2 = 29, what is the value of (x-y)^2 (1) xy = 10 [#permalink]

### Show Tags

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.

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.
_________________
Current Student
Status: DONE!
Joined: 05 Sep 2016
Posts: 398
Re: If x^2 + y^2 = 29, what is the value of (x-y)^2 (1) xy = 10 [#permalink]

### Show Tags

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

### Show Tags

11 Oct 2017, 07:28
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
Math Expert
Joined: 02 Sep 2009
Posts: 47032
Re: If x^2 + y^2 = 29, what is the value of (x-y)^2 (1) xy = 10 [#permalink]

### Show Tags

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

Welcome to the Club.

I have to say the question is not clear. Especially the highlighted part. Next, we have specific rules of posting on the forum (https://gmatclub.com/forum/rules-for-po ... 33935.html). Please read carefully and re-post accordingly. Thank you.
_________________
Re: If x^2 + y^2 = 29, what is the value of (x-y)^2 (1) xy = 10   [#permalink] 11 Oct 2017, 07:35

Go to page   Previous    1   2   [ 24 posts ]

Display posts from previous: Sort by

# Events & Promotions

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.