BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Inequality

Expert replies
Source: — Data Sufficiency |

by Anju@Gurome » Fri Mar 15, 2013 8:37 am
paresh_patil wrote:Is x>y>z?
1) x-y = |x-z| + |z-y|
2) x>y
Statement 1: Note that, |x - z| ≥ 0 and |z - y| ≥ 0
Hence, (x - y) ≥ 0 ---> x ≥ y
Hence, (x - y) = |x - y|

Now, the equation can be interpreted as the sum of the distances of z from x and y on the number line is equal to the distance between x and y.

This is possible only if z is between x and y on the number line or x = y = z.
In either case, the answer to the question is NO.

Sufficient

Statement 2: No information about z.

Not sufficient

The correct answer is A.
Anju Agarwal
Quant Expert, Gurome

Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.

§ GMAT with Gurome § Admissions with Gurome § Career Advising with Gurome §
Join the discussion

by GMATGuruNY » Fri Mar 15, 2013 8:57 am
paresh_patil wrote:Is x>y>z?
1) x-y = |x-z| + |z-y|
2) x>y
|a-b| = the DISTANCE between a and b.

Statement 1: x-y = |x-z| + |z-y|
In other words:
x-y = (the distance between x and z) + (the distance between z and y).

Draw a NUMBER LINE.
If x>y>z, we get:
Z <---------------> Y <-------(x-y)------> X

Here, x-y is LESS THAN the distance between x and z, violating the requirement that x-y = (the distance between x and z) + (the distance between z and y).
Thus, it is not possible that x>y>z.
SUFFICIENT.

Statement 2: x>y
No information about z.
INSUFFICIENT.

The correct answer is A.
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
Join the discussion