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

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Director

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If xy + z = x(y+z), which of the following must be true? [#permalink]

23 Jun 2007, 02:33

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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

Sorry! I edited the choice D and E. it is not "and".

Last edited by LM on 23 Jun 2007, 06:04, edited 1 time in total.

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23 Jun 2007, 04:23

XY + Z = X(Y+Z)

XY + Z = XY + XZ

X = Z/Z (Z cannot be zero)

X = 1

we are left with B,D - I don't see the difference

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23 Jun 2007, 04:51

KillerSquirrel wrote:

XY + Z = X(Y+Z)

XY + Z = XY + XZ

X = Z/Z (Z cannot be zero)

X = 1

we are left with B,D - I don't see the difference

How do you say - Z can't be zero.
Substitute zero in both sides of XY + Z = XY + XZ
The equation is satisfied.
Take example : if I say 5x = y , would you say that x can't be zero because 5 = y/x . But the fact is y and x both can be zero.

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23 Jun 2007, 04:57

vshaunak@gmail.com wrote:

KillerSquirrel wrote:

XY + Z = X(Y+Z)

XY + Z = XY + XZ

X = Z/Z (Z cannot be zero)

X = 1

we are left with B,D - I don't see the difference

I stand corrected :roll:

Senior Manager

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23 Jun 2007, 05:03

The solution should be:
=> XY + Z = X(Y+Z)
=> XY + Z = XY + XZ
=> Z*(X-1)=0
=> Z=0;X=1

Answer: E

We can't do this

KillerSquirrel wrote:

XY + Z = X(Y+Z)

XY + Z = XY + XZ

X = Z/Z (Z cannot be zero)

X = 1

we are left with B,D - I don't see the difference

specifically because Z could be zero.

Director

Joined: 03 Sep 2006

Posts: 910

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23 Jun 2007, 06:06

sumande wrote:

The solution should be:
=> XY + Z = X(Y+Z)
=> XY + Z = XY + XZ
=> Z*(X-1)=0
=> Z=0;X=1

Answer: E

We can't do this

KillerSquirrel wrote:

XY + Z = X(Y+Z)

XY + Z = XY + XZ

X = Z/Z (Z cannot be zero)

X = 1

we are left with B,D - I don't see the difference

:?

specifically because Z could be zero.

Yours is the best explanation. Requires less time to think and faster to reach the answer! Thanks

[#permalink] 23 Jun 2007, 06:06

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

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

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