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# If (x + 2)/(y - 3) = 0, which of the following must be true?

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If (x + 2)/(y - 3) = 0, which of the following must be true?  [#permalink]

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26 Aug 2018, 05:06
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73% (00:42) correct 27% (01:03) wrong based on 56 sessions

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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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Re: If (x + 2)/(y - 3) = 0, which of the following must be true?  [#permalink]

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26 Aug 2018, 05:15
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Bunuel 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 $$y \neq 3$$

which of the following must be true?

$$\frac{x+2}{y-3}=0$$ ==> x+2=0

Hence x=-2

Eliminate A,B & C

If y=3 It is undifened

Hence E
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Re: If (x + 2)/(y - 3) = 0, which of the following must be true?  [#permalink]

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26 Aug 2018, 05:17
Top Contributor
Bunuel 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

Cheers,
Brent
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Re: If (x + 2)/(y - 3) = 0, which of the following must be true?  [#permalink]

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26 Aug 2018, 06:58
Bunuel 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 $$y \neq 3$$

$$\frac{x+2}{y-3}=0$$

Here must be $$\frac{0}{y-3}=0$$, as $$y - 3$$ can not be $$0$$, as anything divided by $$0$$ is undefined...

Thus, $$x + 2 = 0$$

So, $$x = - 2$$ , Options (D) and (E) remains

Further $$y - 3$$ cannot be $$0$$, so cannot be $$3$$, Answer must be (E)
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Re: If (x + 2)/(y - 3) = 0, which of the following must be true?  [#permalink]

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26 Aug 2018, 12:55
Bunuel 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 $$y \neq 3$$

Denominator can be 0. Our ultimate result is 0. So it is clear that x must be -2 and y can't 3.

The best answer is E.
Re: If (x + 2)/(y - 3) = 0, which of the following must be true? &nbs [#permalink] 26 Aug 2018, 12:55
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# If (x + 2)/(y - 3) = 0, which of the following must be true?

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