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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)


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Gennadiy

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


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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


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Gennadiy

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


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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?


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Gennadiy

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


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