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

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

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New post 02 May 2018, 00:55
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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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New post 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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New post 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.

Can you please explain?
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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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New post 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.

Can you please explain?


The OA is D. Edited. Thank you.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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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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New post 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. \(x?(y-1)\)


Let’s analyze each answer choice.

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.

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

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New post 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
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The operation ? is defined for all integers x and y as x?y = xy - y. &nbs [#permalink] 07 Oct 2018, 10:42
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