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# The operation ? is deﬁned for all integers x and y as x?y = xy - y.

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Math Expert
Joined: 02 Sep 2009
Posts: 52971
The operation ? is deﬁned for all integers x and y as x?y = xy - y.  [#permalink]

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02 May 2018, 00:55
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Difficulty:

35% (medium)

Question Stats:

68% (01:33) correct 32% (02:01) wrong based on 99 sessions

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The operation ? is deﬁned for all integers x and y as $$x?y = xy - y$$. If x and y are positive integers, which of the following CANNOT be zero?

A. $$x?y$$

B. $$y?x$$

C. $$(x-1)?y$$

D. $$(x+1)?y$$

E. $$x?(y-1)$$

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Re: The operation ? is deﬁned for all integers x and y as x?y = xy - y.  [#permalink]

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02 May 2018, 04:30
Bunuel wrote:
The operation ? is deﬁned for all integers x and y as $$x?y = xy - y$$. If x and y are positive integers, which of the following CANNOT be zero?

A. $$x?y$$

B. $$y?x$$

C. $$(x-1)?y$$

D. $$(x+1)?y$$

E. $$x?(y-1)$$

Provide that , $$x?y = xy - y$$ = $$x(y-1)$$
A. $$x?y$$ ===========>=$$xy-y$$=$$x(y-1)$$.............................................. is 0 when y=1
B. $$y?x$$ ===========>=$$yx-x$$ =$$y(x-1)$$............................................. is 0 when x=1
C. $$(x-1)?y$$ =====>=$$(x-1)y-y$$ =$$xy-y-y$$ =$$(xy-2y)$$ =$$y(x-2)$$ ...... is 0 when x=2
D. $$(x+1)?y$$ =====>=$$(x+1)y-y$$ =$$xy+y-y$$ =$$xy$$ ............................ can not be 0 as x, y are both positive integer
E. $$x?(y-1)$$ =====>=$$x(y-1)-(y-1)$$ =$$(x-1)(y-1)$$ .............................. is 0 when x=1 or y=1 or both

Hence the answer would be D
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Re: The operation ? is deﬁned for all integers x and y as x?y = xy - y.  [#permalink]

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02 May 2018, 21:20
Bunuel wrote:
The operation ? is deﬁned for all integers x and y as $$x?y = xy - y$$. If x and y are positive integers, which of the following CANNOT be zero?

A. $$x?y$$

B. $$y?x$$

C. $$(x-1)?y$$

D. $$(x+1)?y$$

E. $$x?(y-1)$$

Hi Bunuel,

I worked out D ($$(x+1)?y$$) as the answer, but the correct answer is marked as E. I do not know whether I am missing anything.

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Re: The operation ? is deﬁned for all integers x and y as x?y = xy - y.  [#permalink]

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02 May 2018, 22:11
GMATisLovE wrote:
Bunuel wrote:
The operation ? is deﬁned for all integers x and y as $$x?y = xy - y$$. If x and y are positive integers, which of the following CANNOT be zero?

A. $$x?y$$

B. $$y?x$$

C. $$(x-1)?y$$

D. $$(x+1)?y$$

E. $$x?(y-1)$$

Hi Bunuel,

I worked out D ($$(x+1)?y$$) as the answer, but the correct answer is marked as E. I do not know whether I am missing anything.

The OA is D. Edited. Thank you.
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Re: The operation ? is deﬁned for all integers x and y as x?y = xy - y.  [#permalink]

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03 May 2018, 09:42
Bunuel wrote:
The operation ? is deﬁned for all integers x and y as $$x?y = xy - y$$. If x and y are positive integers, which of the following CANNOT be zero?

A. $$x?y$$

B. $$y?x$$

C. $$(x-1)?y$$

D. $$(x+1)?y$$

E. $$x?(y-1)$$

A) x?y

x?y = 0

xy - y = 0

y(x - 1) = 0

y = 0 or x = 1

Since y can’t be 0, then x = 1. However, as long as x = 1, regardless of what y is, we will have x?y = 0. Thus, A is not the answer.

B) y?x

y?x = 0

yx - x = 0

x(y - 1) = 0

x = 0 or y = 1

Since x can’t be 0, then y = 1. However, as long as y = 1, regardless of what x is, we will have y?x = 0. Thus, B is not the answer.

C) (x - 1)?y

(x - 1)?y = 0

(x - 1)y - y = 0

xy - 2y = 0

y(x - 2) = 0

y = 0 or x = 2

Since y can’t be 0, then x = 2. However, as long as x = 2, regardless of what y is, we will have (x - 1)?y = 0. Thus C is not the answer.

D) (x + 1)?y

(x + 1)?y = 0

(x + 1)y - y = 0

xy = 0

y = 0 or x = 0

We see that the only way (x + 1)?y can be 0 is if y = 0 or x = 0. However, we are given that both x and y are positive integers. Therefore, there is no way (x + 1)?y can be 0. Thus, D is the answer.

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The operation ? is deﬁned for all integers x and y as x?y = xy - y.  [#permalink]

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07 Oct 2018, 10:42
Bunuel wrote:
The operation ? is deﬁned for all integers x and y as $$x?y = xy - y$$. If x and y are positive integers, which of the following CANNOT be zero?

A. $$x?y$$

B. $$y?x$$

C. $$(x-1)?y$$

D. $$(x+1)?y$$

E. $$x?(y-1)$$

option A and B are similar and option C and E are similar

So option D has to be the answer...odd one out
The operation ? is deﬁned for all integers x and y as x?y = xy - y.   [#permalink] 07 Oct 2018, 10:42
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