Absolute value

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Uri: Master | Next Rank: 500 Posts; Posts: 229; Joined: Tue Jan 13, 2009 6:56 am; Thanked: 8 times; GMAT Score:700

by Uri » Wed May 06, 2009 6:08 am

Is |x-z|>|x-y|?
1) |z|>|y|
2) 0>x

OA: [spoiler](E)[/spoiler]

What is the best way to attack this type of problem, where the absolute value is considered in both the sides? I find that picking numbers is very much time-consuming. Is there any other way out?

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Source: Beat The GMAT — Data Sufficiency | Wed May 06, 2009 6:08 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

Re: Absolute value

by Brent@GMATPrepNow » Wed May 06, 2009 8:36 am

Uri wrote:Is |x-z|>|x-y|?
1) |z|>|y|
2) 0>x

OA: [spoiler](E)[/spoiler]

What is the best way to attack this type of problem, where the absolute value is considered in both the sides? I find that picking numbers is very much time-consuming. Is there any other way out?

One thing that's important to recognize is that |k| is the distance from k to 0 on the number line.
Similarly, |x-z| gives us the distance between x and z on the number line and |x-y| gives us the distance between x and y on the number line.

So, the question can be reworded as "On the number line, is z further away from x than y is?"
From here, you can use the number line and try different values of x, y, and z to determine the answer. Using the number line approach, will give you a nice visual to work with.

Brent Hanneson - Creator of GMATPrepNow.com

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Uri: Master | Next Rank: 500 Posts; Posts: 229; Joined: Tue Jan 13, 2009 6:56 am; Thanked: 8 times; GMAT Score:700

by Uri » Thu May 07, 2009 4:52 am

thanks for the valuable suggestion, brent!
following your advice, i have worked out the problem in the below-mentioned way. hope i have applied your suggestion correctly!

The question asks, “Is z further from x than y is from x?”
St 1: Until we know the position of x, we can not say for sure which one is nearer to x. Consider three numbers. We know that one number is greater than the other. But if we don’t know the position of the third number, we can not be certain which of these two numbers will be nearer to the third one. So, this statement is insufficient.
St 2: We know that x is negative. But if we don’t know the position of the other two numbers, we can not be sure which one is nearer to x.
Consider St 1 and St 2 together. We know that z is further from zero than y is from zero. We also know that x is negative. Now if both y and z are negative, then z must be further than x, but if z is negative and y is positive, then depending on the value of x, any one of y or z can be nearer to x. Thus both the statements together are also not sufficient.

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