Inequalities: Testing positives and negatives

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meanjonathan: Senior | Next Rank: 100 Posts; Posts: 42; Joined: Mon Jan 10, 2011 6:57 pm; Thanked: 6 times

by meanjonathan » Sun Jan 23, 2011 11:18 am

The best way to solve a problem like this is to test positives and negatives in the various cases, right?

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

(1) a < 0
(2) ab 0

What's the best way to do this without spending more than 2 minutes? Are there any shortcuts?

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Source: Beat The GMAT — Data Sufficiency | Sun Jan 23, 2011 11:18 am

Night reader: Legendary Member; Posts: 1337; Joined: Sat Dec 27, 2008 6:29 pmFollowed by: 10 members; Thanked: 127 times

by Night reader » Sun Jan 23, 2011 11:30 am

meanjonathan wrote:The best way to solve a problem like this is to test positives and negatives in the various cases, right?

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

(1) a < 0
(2) ab 0

What's the best way to do this without spending more than 2 minutes? Are there any shortcuts?

traditional way would be just simplify this question and apply mod/sign concept --> a>b OR a>-b, now question

Is |b|<(a-b)/a -->
b<(a-b)/a OR b<-(a-b)/a --> 1-b/a>b OR b/a - 1>b ?

Possibly you will benefit from testing the numbers than solving inequality. After several seconds of processing the question it becomes evident that by testing the numbers we win time and keep closer the correct answer

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VivianKerr: GMAT Instructor; Posts: 1035; Joined: Fri Dec 17, 2010 11:13 amFollowed by: 365 members; Location: Los Angeles, CA; Thanked: 474 times

by VivianKerr » Wed Jan 26, 2011 8:46 pm

Picking numbers is absolutely the way to go on this one. Since it's a "yes/no" question, we realize that all we have to do to prove a statement insufficient is find one set of numbers that give us a "yes" and one set of numbers that give us a "no." That way we aren't simply choosing random numbers at random, but with 2 goals in mind.

When I see variables on the GMAT, I write down "+ - frac 0" on my scratch pad and cross them off once I try one of the sets. It's helpful to remember that variables are not always going to be positive integers! Sometimes choosing 0, 1 or a fraction will produce the desired result! [/b]

Vivian Kerr
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Former Kaplan and Grockit instructor, freelance GMAT content creator, now offering affordable, effective, Skype-tutoring for the GMAT at $150/hr. Contact: [email protected]

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meanjonathan: Senior | Next Rank: 100 Posts; Posts: 42; Joined: Mon Jan 10, 2011 6:57 pm; Thanked: 6 times

by meanjonathan » Wed Jan 26, 2011 9:16 pm

Thanks Vivian!

I wish I could see exactly how you set up your page.

Do you routinely test for negative fractions too?
Do you construct a little matrix so you can keep track of your work?
Any other details you can share about your strategy in solving problems like these?

--M.

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VivianKerr: GMAT Instructor; Posts: 1035; Joined: Fri Dec 17, 2010 11:13 amFollowed by: 365 members; Location: Los Angeles, CA; Thanked: 474 times

by VivianKerr » Wed Jan 26, 2011 9:48 pm

Hey Jonathan,

I usually find that negative fractions aren't necessary. Once I've tried one or two sets, it becomes clear to me whether a statement is sufficient or not.

I usually pick numbers like 0, 1, 2, -1, 1/2. I don't make a matrix, but I write down each set I choose and the given result. My "goal" is to get a YES and a NO written down under each statement. As soon as I've got that I can cross off the corresponding answer choices. This is ONLY for "yes/no" DS questions, by the way. Slightly different for "value" questions.

The best way is to develop a use of scratch paper that is super-organized and methodical and works for you. When you study, esp. if you are just starting, aim to write down TOO much and take TOO long. You'll streamline later on.

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