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

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Casey1985
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x - y = 5? (1) x*y = y(y + 5) (2) xy ≠ 0 [#permalink] New post   31 Jan 2020, 22:00
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x - y = 5?

(1) x*y = y(y + 5)
(2) xy ≠ 0
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C
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GMATinsight
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Re: x - y = 5? (1) x*y = y(y + 5) (2) xy ≠ 0 [#permalink] New post   31 Jan 2020, 23:00
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Casey1985 wrote:
x-y = 5?
1) x*y=y(y+5)
2) xy ≠ 0


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
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Bunuel
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Re: x - y = 5? (1) x*y = y(y + 5) (2) xy ≠ 0 [#permalink] New post   01 Feb 2020, 02:10
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GMATinsight wrote:
Casey1985 wrote:
x-y = 5?
1) x*y=y(y+5)
2) xy ≠ 0


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


___________________
Edited the OA. Thank you.
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Re: x - y = 5? (1) x*y = y(y + 5) (2) xy ≠ 0 [#permalink] New post   20 Feb 2020, 07:21
When you try to solve statement 1 algebraically you get \(x-y=5\). Shouldn't statement 1 be sufficient?

\(x*y = y(y + 5)\)
\(x=\frac{y(y + 5)}{y}\)
\(x=y+5\)
\(x-y=5\)
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Re: x - y = 5? (1) x*y = y(y + 5) (2) xy ≠ 0 [#permalink] New post   20 Feb 2020, 18:47
Casey1985 wrote:
x - y = 5?

(1) x*y = y(y + 5)
(2) xy ≠ 0


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.
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Re: x - y = 5? (1) x*y = y(y + 5) (2) xy ≠ 0 [#permalink] New post   20 Feb 2020, 23:57
Casey1985 wrote:
x - y = 5?

(1) x*y = y(y + 5)
(2) xy ≠ 0


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.
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Re: x - y = 5? (1) x*y = y(y + 5) (2) xy ≠ 0 [#permalink] New post   09 Mar 2020, 14:35
Casey1985 wrote:
x - y = 5?

(1) x*y = y(y + 5)
(2) xy ≠ 0


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.
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Re: x - y = 5? (1) x*y = y(y + 5) (2) xy ≠ 0 [#permalink] New post   28 Apr 2020, 00:20
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)
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Re: x - y = 5? (1) x*y = y(y + 5) (2) xy ≠ 0 [#permalink] New post   28 Apr 2020, 00:26
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ChairmanThe wrote:
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)


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.
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Re: x - y = 5? (1) x*y = y(y + 5) (2) xy ≠ 0 [#permalink]
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