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which of the following must be true?
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Carcass
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Joined: 18 Apr 2015
Posts: 15621
GRE 1: Q160 V160
which of the following must be true? [#permalink] New post  24 Aug 2018, 15:27
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If \(\frac{x+2}{y-3}=0\), which of the following must be true?


(A) x = 2 and y = 3

(B) x= 2 and \(y \neq 3\)

(C) x = 0 and y = 0

(D) x = -2 and y = 3

(E) x = -2 and \(y \neq 3\)
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GreenlightTestPrep
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Re: which of the following must be true? [#permalink] New post  25 Aug 2018, 07:47
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Carcass wrote:
If \(\frac{x+2}{y-3}=0\), which of the following must be true?


(A) x = 2 and y = 3

(B) x= 2 and \(y \neq 3\)

(C) x = 0 and y = 0

(D) x = -2 and y = 3

(E) x = -2 and \(y \neq 3\)


In order for (x+2)/(y-3) = 0, it must be the case that the numerator, x+2, is equal to zero.
If x + 2 = 0, then x = -2

Check the answer choices.....
We can ELIMINATE A, B and C, but are still left with D and E

IMPORTANT: 0/0 does NOT equal zero.

This means, for (x+2)/(y-3) to equal 0, the denominator CANNOT equal 0
In other words, y-3 CANNOT equal 0
So, y CANNOT equal 3

Answer: E

Cheers,
Brent
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