x - y = 5? (1) x*y = y(y + 5) (2) xy ≠ 0

Question

x - y = 5?

(1) x*y = y(y + 5)
(2) xy ≠ 0

GMATinsight · Answer

Question: Is x-y = 5?

Statement 1 : x*y=y(y+5) 
i.e. either y = 0 (NO) . or x = y+5 (YES) hence

NOT SUFFICIENT

Statement 2 : xy ≠ 0

Values of x and y are unknown hence

NOT SUFFICIENT

Combining

y ≠0 i.e. x=y+5 i,e. x-y = 5

SUFFICIENT

Answer: Option C

Casey1985   Bunuel  The answers mentioned with question seems incorrect. Correct answer must be option C

Bunuel · Answer

___________________
Edited the OA. Thank you.

mjsoriano · Answer

When you try to solve statement 1 algebraically you get  x-y=5 . Shouldn't statement 1 be sufficient?

x*y = y(y + 5) 
 x=\frac{y(y + 5)}{y} 
 x=y+5 
 x-y=5

minustark · Answer

1) x*y = y (y+5) or, x = y + 5. so x - y = 5 . apparently it seems true but if x and y are both 0, then this statement holds true but in that case x - y =0. so not sufficient.

2) it denotes neither x nor y is 0. but it is not sufficient to prove x - y = 5.

together, x and y are non-zero numbers, so x - y = 5. sufficient

C is the answer.

CAMANISHPARMAR · Answer

Nice question!

St 2 is clearly insufficient.

St 1, if y = 0 and x = 5 then the ans is yes; however if y = 0 and x = 10 then the ans is "no". St 1 is insufficient

Combining 1 and 2 gives a clear answer yes.

Option C is the correct answer.

OhMy · Answer

The question asks whether  5+y-x = 0 ?

Statement (1):  
 x*y = y(y + 5) 
 0 = y(y+5-x) 
Means, that either 0 or (y+5-x) or both of them are equal to zero.
 Not Sufficient.

Statement (2):  
x as well as y is not equal to zero. Does not help much for the equation in the question stem.
 Not sufficient.

Combined:  
Since we now from (2) that x and y are not zero, Statement (1) actually tells us that  (y+5-x)  has to be equal to zero. This answers the question.
 Sufficient.

ChairmanThe · Answer

why can't we just divide both sides by Y? Do we really care about the sign here since it is a number divided by itself (so will always equal to 1)

Bunuel · Answer

You cannot reduce x*y = y(y + 5) by y because y can be 0 and we cannot divide by 0. By doing so you loose a root (a possible solution), namely y = 0.

Never reduce equation by variable (or expression with variable), if you are not certain that variable (or expression with variable) doesn't equal to zero. We cannot divide by zero.

x - y = 5? (1) x*y = y(y + 5) (2) xy ≠ 0

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GMAT Data Sufficiency (DS) Questions

x - y = 5? (1) x*y = y(y + 5) (2) xy ≠ 0

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