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GMAT PREP I NUMBER PROPERTY

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GMAT PREP I NUMBER PROPERTY

by pkw209 » Tue Dec 29, 2009 10:26 am
Hey all,

This one should be simple but I don't understand why the answer isn't A. A brief explanation would be very much appreciated. Thanks!

61) 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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by anu009 » Tue Dec 29, 2009 11:14 am
xy +z = xy+xz
now xz = z
in that case either x can ne 1 or z can be 0
the option E gives the answer
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by Stuart@KaplanGMAT » Tue Dec 29, 2009 8:30 pm
anu009 wrote:xy +z = xy+xz
now xz = z
in that case either x can ne 1 or z can be 0
the option E gives the answer
To finish up the algebra:

xz = z

xz - z = 0

z(x - 1) = 0

z = 0 or x = 1
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by pkw209 » Wed Dec 30, 2009 11:55 am
fantastic, thanks guys.
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by pkw209 » Wed Dec 30, 2009 12:03 pm
while i see it can be solved algebraically, how come x=0 and z=0 doesn't work?

no matter what I plug in for y won't both sides be 0?
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by Testluv » Wed Dec 30, 2009 2:11 pm
pkw209 wrote:while i see it can be solved algebraically, how come x=0 and z=0 doesn't work?

no matter what I plug in for y won't both sides be 0?
x=0 and z=0 do "work". That means x COULD be 0 while z COULD be 0. But this is a MUST be true question. So, we need to find a necessary solution. Choice A is a possible but not a necessary solution.
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by pkw209 » Wed Dec 30, 2009 2:21 pm
Thanks. Would it be correct to assume that for all must be true questions, you need to solve algebraically to get the answer?
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by Testluv » Wed Dec 30, 2009 2:34 pm
pkw209 wrote:Thanks. Would it be correct to assume that for all must be true questions, you need to solve algebraically to get the answer?
No, not necessarily. You could have picked numbers but you would need to check every answer choice, elimintaing impossible choices. Then, you would have narrowed it down A and E. At that point you would have to ask yourself which HAS to be true.

Because this is a must be true question, we could have been partial to the choices that say "or" rather than semicolon (semicolon is just "and").

(This is because an "and" is more likely to be something that could be false compared to an "or".)
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by pkw209 » Wed Dec 30, 2009 2:36 pm
Thanks, Testluv. Extremely helpful response as usual :)
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