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

 It is currently 23 Sep 2018, 09:14

### 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 xy = 7 and x – y = 7, then x² +

Author Message
TAGS:

### Hide Tags

CEO
Joined: 12 Sep 2015
Posts: 2883
If xy = 7 and x – y = 7, then x² +  [#permalink]

### Show Tags

17 Feb 2017, 09:55
3
Top Contributor
6
00:00

Difficulty:

45% (medium)

Question Stats:

65% (01:06) correct 35% (01:25) wrong based on 164 sessions

### HideShow timer Statistics

If xy = 7 and x – y = 7, then x² + y² =

(A) 35
(B) 42
(C) 49
(D) 56
(E) 63

* Kudos for all correct solutions

_________________

Brent Hanneson – GMATPrepNow.com

Intern
Joined: 08 Aug 2016
Posts: 18
Re: If xy = 7 and x – y = 7, then x² +  [#permalink]

### Show Tags

17 Feb 2017, 10:13
4
1
(x-y)^2= x^2 + y^2 - 2xy
7^2 = x^2 + y^2 -2*7
x^2 + y^2 = 49+14
x^2 + y^2 = 63

Sent from my Redmi Note 3 using GMAT Club Forum mobile app
_________________

कर्मणयेवाधिकारस्ते मा फलेषु कदाचन|

##### General Discussion
CEO
Joined: 12 Sep 2015
Posts: 2883
Re: If xy = 7 and x – y = 7, then x² +  [#permalink]

### Show Tags

22 Mar 2017, 14:43
3
Top Contributor
1
GMATPrepNow wrote:
If xy = 7 and x – y = 7, then x² + y² =

(A) 35
(B) 42
(C) 49
(D) 56
(E) 63

The important thing to recognize here is that if we square (x - y), we get a x² term and a y² term. We also get an extra xy term, but that's okay, because we're given some information about the product xy.

So, take: x – y = 7 and...
Square both sides: (x - y)² = 7²
Expand: x² - 2xy + y² = 49
Since we're told xy = 7, we'll replace xy with 7 to get: x² - 2(7) + y² = 49
Simplify: x² - 14 + y² = 49
Add 14 to both sides: x² + y² = 63

RELATED VIDEO

_________________

Brent Hanneson – GMATPrepNow.com

Senior Manager
Joined: 23 Feb 2015
Posts: 419
Re: If xy = 7 and x – y = 7, then x² +  [#permalink]

### Show Tags

22 Mar 2017, 18:34
GMATPrepNow wrote:
If xy = 7 and x – y = 7, then x² + y² =

(A) 35
(B) 42
(C) 49
(D) 56
(E) 63

* Kudos for all correct solutions

x² + y²=(x-y)²+2xy
=7²+2*7
=49+14
=63
So, the correct choice is
_________________

“The heights by great men reached and kept were not attained in sudden flight but, they while their companions slept, they were toiling upwards in the night.”

Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4033
Location: India
GPA: 3.5
Re: If xy = 7 and x – y = 7, then x² +  [#permalink]

### Show Tags

23 Mar 2017, 08:47
GMATPrepNow wrote:
If xy = 7 and x – y = 7, then x² + y² =

(A) 35
(B) 42
(C) 49
(D) 56
(E) 63

* Kudos for all correct solutions

$$( x - y )^2 + 2xy = x^2 + y^2$$

Or, $$7^2 + 2*7 = x^2 + y^2$$

Or, $$49 + 14 = x^2 + y^2$$

Or, $$x^2 + y^2 = 63$$

Thus, answer must be (E) 63...
_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Retired Moderator
Joined: 19 Mar 2014
Posts: 961
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5
Re: If xy = 7 and x – y = 7, then x² +  [#permalink]

### Show Tags

16 Jul 2017, 13:09
If xy = 7 and x – y = 7, then x² + y² =

$$(x - y)^2 = x^2 - 2xy + y^2$$

$$x^2 + y^2 = (x - y)^2 + 2xy$$

$$x^2 + y^2 = (7)^2 + 2 * 7$$

$$x^2 + y^2 = 49 + 14$$

$$x^2 + y^2 = 63$$

_________________

"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent."

Best AWA Template: https://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html#p470475

Non-Human User
Joined: 09 Sep 2013
Posts: 8157
Re: If xy = 7 and x – y = 7, then x² +  [#permalink]

### Show Tags

23 Aug 2018, 11:44
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: If xy = 7 and x – y = 7, then x² + &nbs [#permalink] 23 Aug 2018, 11:44
Display posts from previous: Sort by

# If xy = 7 and x – y = 7, then x² +

## 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®.