Algebra

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Thonk02: Junior | Next Rank: 30 Posts; Posts: 18; Joined: Fri Jan 30, 2009 1:30 pm

by Thonk02 » Mon Jul 06, 2009 4:27 pm

Whatt is value of: (X+Y) ^2
_________
(X-Y)^2

1. X^2 + Y^2 = 3XY
2. XY = 3

Any ideas?

answer is D.

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Source: Beat The GMAT — Data Sufficiency | Mon Jul 06, 2009 4:27 pm

GMATQuantCoach: Senior | Next Rank: 100 Posts; Posts: 44; Joined: Sun Jun 28, 2009 8:58 am; Location: Online; Thanked: 13 times; GMAT Score:51

by GMATQuantCoach » Mon Jul 06, 2009 7:24 pm

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

Re: Algebra

by Ian Stewart » Mon Jul 06, 2009 7:54 pm

Thonk02 wrote:Whatt is value of: (X+Y) ^2
_________
(X-Y)^2

1. X^2 + Y^2 = 3XY
2. XY = 3

Any ideas?

answer is D.

I expect the question means to ask for the value of:

(x+y)^2
(x-y)^2

and if so, the answer certainly is not D.

If you expand the top and bottom, the expression is equal to:

x^2 + 2xy + y^2
x^2 - 2xy + y^2

And using Statement 1, we can replace x^2 + y^2 on the top and bottom to get:

3xy + 2xy
3xy - 2xy

= 5/1 = 5

Using Statement 2, we won't get the necessary cancellation, so the Statement is insufficient. To be sure, you can plug in any pair of values which satisfy xy = 3; if x = 3 and y = 1, the expression is equal to 4, whereas if x = 2 and y = 3/2, the expression is equal to 49.

So unless I've misunderstood the typography in the question, the answer should be A.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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tohellandback: Legendary Member; Posts: 752; Joined: Sun May 17, 2009 11:04 pm; Location: Tokyo; Thanked: 81 times; GMAT Score:680

Re: Algebra

by tohellandback » Mon Jul 06, 2009 8:45 pm

Ian Stewart wrote:
Thonk02 wrote:Whatt is value of: (X+Y) ^2
_________
(X-Y)^2

1. X^2 + Y^2 = 3XY
2. XY = 3

Any ideas?

answer is D.
I expect the question means to ask for the value of:

(x+y)^2
(x-y)^2

and if so, the answer certainly is not D.

If you expand the top and bottom, the expression is equal to:

x^2 + 2xy + y^2
x^2 - 2xy + y^2

And using Statement 1, we can replace x^2 + y^2 on the top and bottom to get:

3xy + 2xy
3xy - 2xy

= 5/1 = 5

Using Statement 2, we won't get the necessary cancellation, so the Statement is insufficient. To be sure, you can plug in any pair of values which satisfy xy = 3; if x = 3 and y = 1, the expression is equal to 4, whereas if x = 2 and y = 3/2, the expression is equal to 49.

So unless I've misunderstood the typography in the question, the answer should be A.

or Thonk has left out "X and Y are positive integers."

The powers of two are bloody impolite!!

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GMAT/MBA Expert

Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

Re: Algebra

by Ian Stewart » Tue Jul 07, 2009 4:18 am

tohellandback wrote: or Thonk has left out "X and Y are positive integers."

If it's a real GMAT question, x and y can't possibly be positive integers - if they were, the two statements would be inconsistent.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

ianstewartgmat.com

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