inequality problem help needed.

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ashish1354: Master | Next Rank: 500 Posts; Posts: 100; Joined: Wed Jul 30, 2008 9:52 am; Thanked: 4 times

by ashish1354 » Thu Mar 05, 2009 12:56 am

31. Is X greater than 1?

(1) X > X^2.

(2) –X < -X^2

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Source: Beat The GMAT — Data Sufficiency | Thu Mar 05, 2009 12:56 am

kamu: Senior | Next Rank: 100 Posts; Posts: 49; Joined: Fri Feb 27, 2009 12:41 amFollowed by: 3 members; Thanked: 44 times

by kamu » Thu Mar 05, 2009 2:06 am

both stems suggest that x<1.
OA : D

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bluementor: Master | Next Rank: 500 Posts; Posts: 418; Joined: Wed Jun 11, 2008 5:29 am; Thanked: 65 times

Re: inequality problem help needed.

by bluementor » Thu Mar 05, 2009 5:16 am

ashish1354 wrote:31. Is X greater than 1?

(1) X > X^2.

(2) –X < -X^2

Statement 1:
x > x^2
x^2 - x < 0
x(x-1) < 0

Either x or (x-1) must be less than 0, and the other must be positive. Clearly x must be positive since its larger than (x-1). The only possible range for x is therefore 0<x<1, which answers the question stem a definite NO. Sufficient.

Statement 2:
-x < -x^2
x^2 -x < 0
x(x-1)<0

Same conclusion can be drawn here as it is done in statement 1. Sufficient.

Choose D.

-BM-

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Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pmFollowed by: 614 members; Location: Toronto; Thanked: 1710 times; GMAT Score:800

Re: inequality problem help needed.

by Stuart@KaplanGMAT » Thu Mar 05, 2009 1:48 pm

ashish1354 wrote:31. Is X greater than 1?

(1) X > X^2.

(2) –X < -X^2

Bluementor's solution is great - just a quick guessing point.

We can multiply both sides of the inequality in (2) to turn it into the inequality in (1); in other words the two statements are identical.

When you have identical statements, we can always eliminate (A), (B) and (C) - so even if we have no clue whether the information is sufficient, we still have a 50/50 shot at the question.

Stuart Kovinsky | Kaplan GMAT Faculty | Toronto

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