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# If (x-5)(y+2) = 0 which of the following must be true?

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If (x-5)(y+2) = 0 which of the following must be true? [#permalink]

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31 Jan 2013, 07:41
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If (x-5)(y+2) = 0 which of the following must be true?

(A) x = y
(B) x > y
(C) x < y
(D) xy = -10
(E) None of the above
[Reveal] Spoiler: OA

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Last edited by Bunuel on 31 Jan 2013, 07:50, edited 1 time in total.
Renamed the topic and edited the question.
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31 Jan 2013, 07:55
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sananoor wrote:
if (x-5)(y+2)=0 which of the following must be true?

(A)X=Y
(b) X>Y
(C)X<Y
(d)XY=-10
e.none of th above

If (x-5)(y+2) = 0 which of the following must be true?

(A) x = y
(B) x > y
(C) x < y
(D) xy = -10
(E) None of the above

From (x-5)(y+2) = 0 it follows that either x=5 or y=-2.

(A) x = y --> not necessarily true. Consider x=5 and y=0.
(B) x > y --> not necessarily true. Consider x=5 and y=10.
(C) x < y --> not necessarily true. Consider x=5 and y=0.
(D) xy = -10 --> not necessarily true. Consider x=5 and y=0.

Thus, none of the statements must be true.

Hope it's clear.

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to the rule #3 (the name of a topic MUST be the first 40 characters (~the first two sentences) of the question).
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Re: If (x-5)(y+2) = 0 which of the following must be true? [#permalink]

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31 Jan 2013, 09:10
i didnt get this how u consider X and Y values when it is given in the question
If (x-5)(y+2) this means that X = 5 and Y = -2
thus XY = -10 and X > Y..
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Re: If (x-5)(y+2) = 0 which of the following must be true? [#permalink]

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31 Jan 2013, 09:20
sananoor wrote:
i didnt get this how u consider X and Y values when it is given in the question
If (x-5)(y+2) this means that X = 5 and Y = -2
thus XY = -10 and X > Y..

(x-5)(y+2) = 0 means that EITHER x=5 OR y=-2. For example, if x=5, then y can be any number. The same way, if y=-2, then x can be any number.
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Re: If (x-5)(y+2) = 0 which of the following must be true? [#permalink]

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31 Jan 2013, 17:08
Bunuel wrote:
sananoor wrote:
i didnt get this how u consider X and Y values when it is given in the question
If (x-5)(y+2) this means that X = 5 and Y = -2
thus XY = -10 and X > Y..

(x-5)(y+2) = 0 means that EITHER x=5 OR y=-2. For example, if x=5, then y can be any number. The same way, if y=-2, then x can be any number.

Bunuel, although your solution is perfect, I would just point out a rewording suggestion on your last comment. (x-5)(y+2) =0 means that x = 5 OR y =-2 (without the EITHER). Obviously both equalities COULD happen simultaneously, but they don't HAVE TO happen simultaneously in order for the equation in stem to be valid
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Re: If (x-5)(y+2) = 0 which of the following must be true? [#permalink]

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31 May 2015, 20:22
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Re: If (x-5)(y+2) = 0 which of the following must be true? [#permalink]

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02 Jun 2015, 08:01
If (x-5)(y+2) = 0 which of the following must be true?

(A) x = y Only one of x = y = 5 or x = y = - 2, or x can be 100 (or any other value, for example and y= -2, making this equation hold true
(B) x > y If x = 5 and y = -2 this is true, but x can be -75 (any value) and y = -2
(C) x < y The same is true for this inequality. If x = 5 y can be any value larger or smaller, or if y = -2 then x can be any value larger or smaller.
(D) xy = -10 This is true when x = 5 and y = -2 but they need not be.
(E) None of the above
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Re: If (x-5)(y+2) = 0 which of the following must be true? [#permalink]

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04 Jun 2015, 11:35
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The ques is really good in wording in the sense that it asks "MUST BE TRUE"
Had the question been "could be true"
then x=5 and y-2 could lead to x>y
Re: If (x-5)(y+2) = 0 which of the following must be true?   [#permalink] 04 Jun 2015, 11:35
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