Absolute Value - Help Please

Expert replies

siddarth: Junior | Next Rank: 30 Posts; Posts: 15; Joined: Tue Aug 12, 2008 7:00 am

by siddarth » Tue Sep 23, 2008 4:27 am

Is |x-z|>|x-y|

1) |z|>|y|
2) 0>x

My solution was as follows:

the original equation will give us 2 results:

a) x-z>x-y => x-z-x+y>0 => y+z>0.
b) -x+z>-x+y => -x+z+x-y>0 => z-y>0.

Now Statement 1 will satisfy both these conditions, so my answer is Statement 1 is enough to answer the question.

Statement 2 by itself is of no help.

The Answer however is E.

Could someone please help me out with this. I always get confused with Absolute Value questions.

Should i instead take numbers and work out such problems.

Thanks

Source: Beat The GMAT — Data Sufficiency | Tue Sep 23, 2008 4:27 am

gdrea3: Junior | Next Rank: 30 Posts; Posts: 21; Joined: Sun Sep 07, 2008 1:30 pm; Thanked: 2 times

by gdrea3 » Tue Sep 23, 2008 4:57 am

Start with the easier statement, (2)--> 0>x INSUFFICIENT
Statement 1 states that the absolute value of z is greater than the absolute value of y, but it doesn't tell us about the value of x-->INSUFFICIENT.

Put the two statements together:
so if 0>x, pick a negative number for x
and if the abolute val of z>absolute val of x, pick positive AND negative #s (remember that # is the absolute value brackets are POSITIVE AFTER YOU DO ANY ADDITION, SUBTRACTION, MULTIPLICATION, etc:

Use -1 for x, -3 for z, and -2 for y:
|x-z|>|x-y| -->|-1+3|>|-1+2| so is 2>1? YES

Use -10 for x,-4 for z, and -2 for y:
|x-z|>|x-y| -->|-10+4|>|-10+2| so is 6>8 NO

BOTH statements together are insufficient

siddarth: Junior | Next Rank: 30 Posts; Posts: 15; Joined: Tue Aug 12, 2008 7:00 am

by siddarth » Tue Sep 23, 2008 5:15 am

Thanks, got it

gdrea3 wrote:Start with the easier statement, (2)--> 0>x INSUFFICIENT
Statement 1 states that the absolute value of z is greater than the absolute value of y, but it doesn't tell us about the value of x-->INSUFFICIENT.

Put the two statements together:
so if 0>x, pick a negative number for x
and if the abolute val of z>absolute val of x, pick positive AND negative #s (remember that # is the absolute value brackets are POSITIVE AFTER YOU DO ANY ADDITION, SUBTRACTION, MULTIPLICATION, etc:

Use -1 for x, -3 for z, and -2 for y:
|x-z|>|x-y| -->|-1+3|>|-1+2| so is 2>1? YES

Use -10 for x,-4 for z, and -2 for y:
|x-z|>|x-y| -->|-10+4|>|-10+2| so is 6>8 NO

BOTH statements together are insufficient

Featured schoolRound 2 closes Jan 7, 2027 58 days left

Chicago Booth

Since 1982, 10 Booth faculty members have received the Nobel Prize in Economic Sciences, more than any other business school.

#3
U.S. News rank: $175,000
Median base salary: 670
Average GMAT Focus: 635
Students in the class

Apply to Booth Visit chicagobooth.edu See the full profile

Photo: Warren LeMay, CC BY-SA 2.0

GMAT Course Reviews

563 reviews

1168 reviews

431 reviews

359 reviews

147 reviews

5/5

5 Star (563 Reviews)

"Target Test Prep is the closest to the official version of the GMAT exam, about 99% accuracy in terms of the quality and quantity of information. The course has excellently created singular sets of focused lessons and tests for every possible topic that one could come across in the official GMAT exam."

"The TTP course maximizes the efficiency of the time you spend studying. It will take time and effort but I could almost guarantee that if you complete the course exactly as it is laid out you will get an amazing score. They also have a very responsive team willing to help with any questions you might have."

"TTP has two things that I think no other test prep company offers: A teaching approach that reinforces understanding and an attitude that will give you the mental preparedness needed to succeed on the test. TTP gives you a deep understanding of the concept you need to know while teaching you how to think."

Write a Review