Pl help solve, thanks

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Nijo: Senior | Next Rank: 100 Posts; Posts: 45; Joined: Thu Jun 12, 2014 8:41 pm; Thanked: 1 times

by Nijo » Sat Aug 09, 2014 9:03 pm

If xy + z = x(y+z), which of the following must be true?
1) x =0 and z =0
2) x=1 and y =1
3) y=1 and z =0
4) x=1 or y=0
5) x =1 or z=0

OA is 5

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Source: Beat The GMAT — Problem Solving | Sat Aug 09, 2014 9:03 pm

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sat Aug 09, 2014 9:22 pm

Nijo wrote:If xy + z = x(y+z), which of the following must be true?
A) x =0 and z =0
B) x=1 and y =1
C) y=1 and z =0
D) x=1 or y=0
E) x =1 or z=0

When posting questions, please use the spoiler function to hide the correct answer. This will allow others to attempt the question without seeing the final answer.

The key word here is must.

Given: xy+z = x(y+z)
Expand: xy+z = xy + xz
Subtract xy from both sides: z = xz
Rearrange: xz - z = 0
Factor: z(x-1) = 0

This tells us that z = 0 or x = 1
Answer: E

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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