 It is currently Sun Sep 22, 2019 3:20 pm

 All times are UTC - 5 hours [ DST ]

 Print view Previous topic | Next topic
Author Message
 Post subject: GMAT Algebra (Data Sufficiency) Posted: Tue Mar 27, 2012 7:46 am Joined: Sun May 30, 2010 3:15 am
Posts: 424
What is the value of x² + y²?
(1) x + y = 4
(2) xy = 2

A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
D. Either statement BY ITSELF is sufficient to answer the question.
E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, meaning that further information would be needed to answer the question.

(C) If we use statement (1) by itself, we can solve it for x. x = 4 – y. The desired sum, x² + y², equals (4 – y)² + y². We do NOT know the value of y. Therefore we do NOT have a definite value of the desired sum. Statement (1) by itself is NOT sufficient.

If we use statement (2) by itself, it implements that y can NOT be 0 and we can solve it for x. x = 2/y. The desired sum, x² + y², is (2/y)² + y². We do NOT know the value of y. Therefore we do NOT have a definite value of the desired sum. Statement (2) by itself is NOT sufficient.

If we use the both statements together, let’s manipulate them a little. First, multiply the second one by 2 to get 2xy = 4. Then square the first one. x² + 2xy + y² = 4². Subtract the second one from the first one to get x² + y² = 16 – 4. Therefore the desired sum equals 16 – 4 = 12. Statements (1) and (2) taken together are sufficient to answer the question, even though neither statement by itself is sufficient. The correct answer is C.
----------
It seems to me that (2) would be correct. If we're looking to find the value of x² + y², all we would need to know is "xy" because:
x² + y² = x² + 2xy + y²
so: x² + y² = -2xy
if xy=2, then -2xy= (-2)2= -4
therefore x² + y² =(-4)

Top Post subject: Re: GMAT Algebra (Data Sufficiency) Posted: Tue Mar 27, 2012 8:14 am Joined: Sun May 30, 2010 2:23 am
Posts: 498

Top Post subject: Re: GMAT Algebra (Data Sufficiency) Posted: Fri Dec 14, 2012 10:52 am Joined: Sun May 30, 2010 3:15 am
Posts: 424
For statement 1,

x + y = 4

so x² + y² can be broken down into (x + y)(x + y) which can be replaced from statement 1. Thus it gives a value of 4 × 4 which is 16. I am confused for this question

Top Post subject: Re: GMAT Algebra (Data Sufficiency) Posted: Fri Dec 14, 2012 11:00 am Joined: Sun May 30, 2010 2:23 am
Posts: 498

Top Post subject: Re: GMAT Algebra (Data Sufficiency) Posted: Fri Jan 25, 2013 4:29 am Joined: Sun May 30, 2010 3:15 am
Posts: 424
How can you combine statement 1 and 2 to make it match? Which product of XY that yields 2 has as sum 4?

In other words, what are X and Y here?

Top Post subject: Re: GMAT Algebra (Data Sufficiency) Posted: Fri Jan 25, 2013 4:50 am Joined: Sun May 30, 2010 2:23 am
Posts: 498

Top Display posts from previous: All posts1 day7 days2 weeks1 month3 months6 months1 year Sort by AuthorPost timeSubject AscendingDescending

 All times are UTC - 5 hours [ DST ]

#### Who is online

Users browsing this forum: No registered users and 4 guests

 You cannot post new topics in this forumYou cannot reply to topics in this forumYou cannot edit your posts in this forumYou cannot delete your posts in this forumYou cannot post attachments in this forum

Search for:
 Jump to:  Select a forum ------------------ GMAT    GMAT: Quantitative Section (Math)    GMAT: Verbal Section    GMAT: Integrated Reasoning    GMAT: General Questions GRE    GRE: Quantitative Reasoning (Math)    GRE: Verbal Reasoning    GRE: General Questions General questions    Other questions Powered by phpBB © 2000, 2002, 2005, 2007 phpBB Group