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

Question

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

Bunuel · Answer

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

sananoor · Answer

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..

Bunuel · Answer

(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.

caioguima · Answer

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

OptimusPrepJanielle · Answer

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

rajgurinder · Answer

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

BrushMyQuant · Answer

(x-5)(y+2) = 0 
=> x = 5, y = -2

(A) x = y,  This is   FALSE   for x  ≠ y
  (B) x > y,  This can be true when x(5) > y(-2), but can be   FALSE   when y = -2 and we don't know the value of x. Or when x = 5 and we don't know the value of y.
 (C) x < y,  This is   FALSE   for x(5) > y(-2) 
 (D) xy = -10 , This can be true when x=5 and y=-2, but can be   FALSE   when y = -2 and we don't know the value of x. Or when x = 5 and we don't know the value of y.
 (E) None of the above ,   TRUE    as not of the options are MUST be true.

So,  Answer will be E 
Hope it helps!

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?

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