If xy + z = x(y + z), which must be true?

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rd85: Senior | Next Rank: 100 Posts; Posts: 39; Joined: Mon May 19, 2008 4:43 am

by rd85 » Thu Jul 16, 2009 2:21 am

If xy + z = x(y + z), which must be true?
a. x = 0; z = 0
b. x = 1; y = 1
c. y = 1; z = 0
d. x = 1 or y = 0
e. x = 1 or z = 0

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Source: Beat The GMAT — Problem Solving | Thu Jul 16, 2009 2:21 am

nitya34: Master | Next Rank: 500 Posts; Posts: 179; Joined: Tue Jan 08, 2008 7:23 pm; Thanked: 11 times; GMAT Score:590

by nitya34 » Thu Jul 16, 2009 3:16 am

z(1-x)=0

B it is?

Many of the great achievements of the world were accomplished by tired and discouraged men who kept on working.

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rd85: Senior | Next Rank: 100 Posts; Posts: 39; Joined: Mon May 19, 2008 4:43 am

by rd85 » Thu Jul 16, 2009 5:07 am

OA is E

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struggling_guy2001: Senior | Next Rank: 100 Posts; Posts: 52; Joined: Tue Jan 27, 2009 9:44 am; Thanked: 4 times

Solution to the above problem..

by struggling_guy2001 » Thu Jul 16, 2009 5:14 am

Given statement:

xy+z= x(y+z)

==> xy+z = xy+xz.

Cancelling xy on both the sides and moving z to other side the equation becomes...

xz-z=0

==> z(x-1) =0

==> z=0 or x=1... Hence E is the answer for the above problem..

Hope it is clear...

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rd85: Senior | Next Rank: 100 Posts; Posts: 39; Joined: Mon May 19, 2008 4:43 am

by rd85 » Fri Jul 17, 2009 5:44 am

Thanks a lot. Appreciate your help!

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