Question involving absolute values

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Auzbee: Senior | Next Rank: 100 Posts; Posts: 77; Joined: Mon Jul 09, 2007 6:54 pm; Location: US of A

Question involving absolute values

by Auzbee » Mon Dec 31, 2007 12:18 pm

If a and b are integers, and |a| > |b|, is a · |b| < a – b?

1. a less than zero
2. ab greater than equal to zero

Would love to see explanation for this one. Can this be cracked in 2 min time?

Last edited by Auzbee on Mon Dec 31, 2007 2:24 pm, edited 1 time in total.

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Source: Beat The GMAT — Data Sufficiency | Mon Dec 31, 2007 12:18 pm

beingAndNothing: Senior | Next Rank: 100 Posts; Posts: 59; Joined: Fri Sep 14, 2007 10:35 am; Thanked: 1 times

by beingAndNothing » Mon Dec 31, 2007 2:20 pm

Auzbee:

I am not sure as to what exactly is the inequality, since formatting is messing up what you've written. Anyways, I would rewrite the inequality by dividing both sides by |b|.
Now a/|b| would be greater than 1 or less than -1 depending on a > 0 or a < 0. Similarly b/|b| = 1 or -1 depending upon the sign.

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Auzbee: Senior | Next Rank: 100 Posts; Posts: 77; Joined: Mon Jul 09, 2007 6:54 pm; Location: US of A

by Auzbee » Mon Dec 31, 2007 2:25 pm

I am not sure as to what exactly is the inequality, since formatting is messing up what you've written.

I have corrected the question in my edit. Let me know your reply.

Thanks

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StarDust845: Master | Next Rank: 500 Posts; Posts: 158; Joined: Mon Dec 03, 2007 8:32 am; Thanked: 7 times

by StarDust845 » Tue Jan 01, 2008 9:38 pm

Is the answer E?

I just put in different values for a and b and arrived at that answer. I wish there were some elegant solution to this problem.

Calista.