OG 11 - Algebra Inequalities - The Beat The GMAT Forum - Expert GMAT Help & MBA Admissions Advice

OG 11 - Algebra Inequalities

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albertrahul: Senior | Next Rank: 100 Posts; Posts: 83; Joined: Wed Jun 04, 2008 3:30 am; Thanked: 4 times

by albertrahul » Mon Jul 07, 2008 3:14 am

Is m != n?
[!= : not equals]

(1) m + n < 0
(2) mn < 0

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Source: Beat The GMAT — Data Sufficiency | Mon Jul 07, 2008 3:14 am

Vignesh.4384: Master | Next Rank: 500 Posts; Posts: 443; Joined: Sat Jun 28, 2008 6:33 pm; Thanked: 5 times

by Vignesh.4384 » Mon Jul 07, 2008 5:07 am

is the answer E ?

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albertrahul: Senior | Next Rank: 100 Posts; Posts: 83; Joined: Wed Jun 04, 2008 3:30 am; Thanked: 4 times

by albertrahul » Mon Jul 07, 2008 5:33 am

Dear Vignesh, would you detail your solution please?
OA is not E.

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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: OG 11 - Algebra Inequalities

by Ian Stewart » Mon Jul 07, 2008 5:48 am

albertrahul wrote:Is m != n?
[!= : not equals]

(1) m + n < 0
(2) mn < 0

Statement 2) is definitely enough on its own: if mn < 0, then m and n have opposite signs, so they can't be equal.

From Statement 1), if m and n are equal and both negative, this will always be true (try m = n = -1). So this is not sufficient; m might be equal to n, and might not.

B.

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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albertrahul: Senior | Next Rank: 100 Posts; Posts: 83; Joined: Wed Jun 04, 2008 3:30 am; Thanked: 4 times

by albertrahul » Mon Jul 07, 2008 5:52 am

Thanks for reply Ian. OG also provides similar solution.

However, I want to know that why can't I assume m = 1/2 and n = 1/2, this also satisfies statement 2.

1/2 * 1/2 = 1/4 < 0

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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

by Ian Stewart » Mon Jul 07, 2008 7:12 am

albertrahul wrote:Thanks for reply Ian. OG also provides similar solution.

However, I want to know that why can't I assume m = 1/2 and n = 1/2, this also satisfies statement 2.

1/2 * 1/2 = 1/4 < 0

1/4 is not less than zero!

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albertrahul: Senior | Next Rank: 100 Posts; Posts: 83; Joined: Wed Jun 04, 2008 3:30 am; Thanked: 4 times

by albertrahul » Mon Jul 07, 2008 9:51 pm

Thanks Ian.
Again, I missed out on basic.

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