Absolute Value question

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Troika: Master | Next Rank: 500 Posts; Posts: 136; Joined: Wed Apr 08, 2009 12:09 pmFollowed by: 1 member; Thanked: 4 times

by Troika » Wed Feb 29, 2012 5:12 pm

Is |x - z| = |y - z|?

1. x = y
2. |x| - z = |y| - z

OA: A

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Source: Beat The GMAT — Data Sufficiency | Wed Feb 29, 2012 5:12 pm

pemdas: Legendary Member; Posts: 1084; Joined: Fri Apr 15, 2011 2:33 pmFollowed by: 21 members; Thanked: 158 times

by pemdas » Wed Feb 29, 2012 5:45 pm

HG10 wrote:Is |x - z| = |y - z|?

1. x = y
2. |x| - z = |y| - z

OA: A

square both sides, Is (x-z)^2=(y-z)^2?
st(1) (y-z)^2=(y-z)^2 Sufficient
st(2) |x|=|y| or x^2=y^2

x^2-2zx+z^2 ... y^2-2zy+z^2 <> y^2-2zx+z^2 ... y^2-2zy+z^z^2
since we don't know about 2zx and 2zy we cannot answer this question, Not Sufficient

a

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Wed Feb 29, 2012 6:56 pm

HG10 wrote:Is |x - z| = |y - z|?

1. x = y
2. |x| - z = |y| - z

OA: A

Question rephrased: Is the distance between x and z equal to the distance between y and z?

Statement 1: x=y
Since x and y are equal, each is the same distance from z.
SUFFICIENT.

Statement 2: |x| - z = |y| - z
Thus, |x| = |y|.
If x=y=1, then x and y are each the same distance from z.
If x=1, y=-1, and z=10, then x and y are not the same distance from z.
INSUFFICIENT.

The correct answer is A.

Note that, by treating this as a DISTANCE problem, we were able to evaluate the statements very efficiently.

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krusta80: Master | Next Rank: 500 Posts; Posts: 143; Joined: Mon Mar 14, 2011 3:13 amFollowed by: 5 members; Thanked: 34 times

by krusta80 » Wed Feb 29, 2012 7:21 pm

HG10 wrote:Is |x - z| = |y - z|?

1. x = y
2. |x| - z = |y| - z

OA: A

Squaring is a nice trick, but you can always just create three non-abs formulas (only one of which need be validated):

a.) x - z = y - z

OR

b.) x - z = z - y

OR

c.) z - x = y - z

(1) x = y

Applying to (a), we get y - z = y - z, which is always true. SUFFICIENT

(2) |x| - z = |y| - z

z's cancel to leave |x| = |y|

x = y, from before we know that this validate's

AND

-x = y

a.) x = y = 0, does NOT always evaluate to true
b.) -z = z, is NEVER true
c.) z = -z, is NEVER true

Given part (2), the main statement works when x = y but does NOT work when x = -y.

INSUFFICIENT

A is the answer

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Troika: Master | Next Rank: 500 Posts; Posts: 136; Joined: Wed Apr 08, 2009 12:09 pmFollowed by: 1 member; Thanked: 4 times

by Troika » Thu Mar 01, 2012 7:06 am

@pemdas, GmatGuruNY & krusta80:

Thank you for explaining this to me!

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