## GMAT PREP 1 QUESTION 3

##### This topic has expert replies
Master | Next Rank: 500 Posts
Posts: 163
Joined: 13 Jan 2015
Thanked: 2 times

### GMAT PREP 1 QUESTION 3

by didieravoaka » Fri Feb 05, 2016 12:25 pm

GMAT Instructor
Posts: 15537
Joined: 25 May 2010
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790
by GMATGuruNY » Fri Feb 05, 2016 12:41 pm
Is |x-y| > |x| - |y| ?
1) y < x
2) xy < 0
One approach is to plot the distances on a NUMBER LINE.

|x|= the distance between x and 0 = the RED segment on the number lines below.
|y| = the distance between y and 0 = the BLUE segment on the number lines below.
|x-y| = the distance BETWEEN X AND Y.

Statement 1: y<x
Case 1: |x| - |y| = RED - BLUE.
|x-y| = RED - BLUE.
Thus, |x-y| = |x| - |y|.

Case 2: |x| - |y| = RED - BLUE.
|x-y| = RED + BLUE.
Thus, |x-y| > |x| - |y|.
INSUFFICIENT.

Statement 2: xy<0
Since x and y have different signs, they are on OPPOSITE SIDES OF 0. In each case:
|x| - |y| = RED - BLUE.
|x-y| = RED + BLUE.
Thus, |x-y| > |x| - |y|.
SUFFICIENT.

The correct answer is B.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

Master | Next Rank: 500 Posts
Posts: 163
Joined: 13 Jan 2015
Thanked: 2 times
by didieravoaka » Sun Feb 07, 2016 5:39 pm
Thanks GuruNY

GMAT Instructor
Posts: 2630
Joined: 12 Sep 2012
Location: East Bay all the way
Thanked: 625 times
Followed by:118 members
GMAT Score:780
by [email protected] » Mon Feb 08, 2016 9:31 am
Another approach:

|x - y| = the distance from x to y.

|x| = the distance from x to 0.

|y| = the distance from y to 0.

So we want to know

Is (distance from x to y) > (distance from x to 0) - (distance from y to 0) ?

S1::

If x > y, consider two options.

i: They're both positive. In this case, |x - y| = |x| - |y|, so the answer is NO.

ii: 0 > x and 0 > y. In this case, |x - y| is positive and |x| - |y| is negative, so the answer is YES.

Conflicting results, so insufficient.

S2::

One is positive, one is negative. Now the distance from x to y is the same as the distance from x to 0, then from 0 to y! In our equations, this can be written as

(the distance from x to y) = (the distance from x to 0) + (the distance from y to 0)

or

|x - y| = |x| + |y|

Since |x| + |y| must now be greater than |x| - |y|, this is SUFFICIENT.

### GMAT/MBA Expert

GMAT Instructor
Posts: 2094
Joined: 04 Dec 2012
Thanked: 1443 times
Followed by:247 members
by ceilidh.erickson » Thu Feb 11, 2016 5:37 pm
Absolute value questions are testing properties of positives & negatives. One way to help translate this question is to create a chart, testing out the possibilities for x and y: Here, we can see that we will only get a "yes" answer to the question when one of the two is positive, and the other negative. If they are both positive or both negative, the two expressions will be equal.

Target question: do x and y have different signs?

(1) y < x

This doesn't tell us anything about signs. Insufficient.

(2) xy < 0

This tells us that they must have different signs. Sufficient.

The answer is B.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education

• Page 1 of 1