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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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New post 26 Aug 2018, 06:06
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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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New post 26 Aug 2018, 06:15
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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New post 26 Aug 2018, 06:17
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

Answer: E

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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New post 26 Aug 2018, 07:58
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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New post 26 Aug 2018, 13:55
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, 13:55
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