Algebra

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danjuma: Senior | Next Rank: 100 Posts; Posts: 89; Joined: Thu Aug 26, 2010 9:29 am; Thanked: 4 times

by danjuma » Mon Sep 20, 2010 10:33 am

1. If XY + Z= X(Y + Z)-which of the following must be true?

a. X=1 and Z=0 b. X=1 and Y=1 c. Y=1 and Z=0 d. X=1 or Y=1 e. X=1 or Z=0

Thanks alot.

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Source: Beat The GMAT — Problem Solving | Mon Sep 20, 2010 10:33 am

niksworth: Legendary Member; Posts: 520; Joined: Mon Jun 14, 2010 10:44 amFollowed by: 6 members; Thanked: 70 times

by niksworth » Mon Sep 20, 2010 10:43 am

XY + Z = X(Y+Z)
=> XY + Z = XY + XZ
=> XY + Z - XY - XZ = 0
=> Z - XZ = 0
=> Z(1 - X) = 0
=> Z = 0 or X = 1

Note that the question asks what must be true and not can be true.

Thus answer is E.

scio me nihil scire

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