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# For all numbers a and b, the operation is defined by ab = a^2 - ab.

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Math Expert
Joined: 02 Sep 2009
Posts: 58382
For all numbers a and b, the operation is defined by ab = a^2 - ab.  [#permalink]

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19 Mar 2015, 06:31
2
11
00:00

Difficulty:

55% (hard)

Question Stats:

65% (02:08) correct 35% (02:21) wrong based on 283 sessions

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For all numbers a and b, the operation @ is defined by a@b = a^2 - ab. If xy ≠ 0, then which of the following can be equal to zero?

I. x@y

II. (xy)@y

III. x@(x + y)

A. II only
B. I and II only
C. I and III only
D. II and III only
E. All of the above

Kudos for a correct solution.

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Re: For all numbers a and b, the operation is defined by ab = a^2 - ab.  [#permalink]

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19 Mar 2015, 21:42
6
3
Bunuel wrote:
For all numbers a and b, the operation @ is defined by a@b = a^2 - ab. If xy ≠ 0, then which of the following can be equal to zero?

I. x@y

II. (xy)@y

III. x@(x + y)

A. II only
B. I and II only
C. I and III only
D. II and III only
E. All of the above

Kudos for a correct solution.

a@b = a^2 - ab = a(a-b)

x and y both are not 0.

I. x@y
x@y = x(x - y)
This will be 0 when either x = 0 (not possible as given), or x - y = 0 i.e. x = y (this is possible)

II. (xy)@y
(xy)@y = xy(xy - y) = xy^2(x - 1)
This will be 0 when either x or y is 0 (not possible) or x = 1 (this is possible)

III. x@(x + y)
x@(x + y) = x(x - (x+y)) = -xy
This will be 0 when at least one of x and y is 0 - (both not possible as given)

Hence only (I) and (II) can be 0. Answer (B)
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##### General Discussion
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Re: For all numbers a and b, the operation is defined by ab = a^2 - ab.  [#permalink]

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19 Mar 2015, 08:26
xy ≠ 0

I. x@y
x^2 - 2xy
xy will always result in a non zero number

II. (xy)@y
(x^2)(y^2) - 2xy^2
If x and y equal 2, this could equal 0

III. x@(x + y)
-(x^2 + 2xy)
If x is 4 and y is -2, this could equal 0

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Re: For all numbers a and b, the operation is defined by ab = a^2 - ab.  [#permalink]

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19 Mar 2015, 18:43
Hi peachfuzz,

I think there's a typo in your work that has impacted ALL of your calculations:

The original 'symbol' in the prompt is....

a@b = a^2 - ab

It looks like your work is based on....

a@b = a^2 - 2ab

Your approach is perfect for this prompt though, so if you make the necessary adjustments to your work, you should get the correct answer.

GMAT assassins aren't born, they're made,
Rich
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Math Expert
Joined: 02 Aug 2009
Posts: 7956
Re: For all numbers a and b, the operation is defined by ab = a^2 - ab.  [#permalink]

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19 Mar 2015, 23:27
1
Bunuel wrote:
For all numbers a and b, the operation @ is defined by a@b = a^2 - ab. If xy ≠ 0, then which of the following can be equal to zero?

I. x@y

II. (xy)@y

III. x@(x + y)

A. II only
B. I and II only
C. I and III only
D. II and III only
E. All of the above

Kudos for a correct solution.

hi,
lets look at the equation in the question and simplify...
a@b = a^2 - ab=a(a-b).... so a@b will be zero if a=b or a=0.. but a cannot be equal to 0.. as per Q, x and y can take any int value except 0...

now lets look at the choices..
I. x@y
when x=y, it will be 0... so ok...

II. (xy)@y
when we put xy=y, it is possible when x=1 and y any integer... so ok again

III. x@(x + y)
when we put x=x+y.... only possibility when y=0 and it is given x and y cannot be 0....so not possible

only l and ll possible ans B....
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Re: For all numbers a and b, the operation is defined by ab = a^2 - ab.  [#permalink]

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20 Mar 2015, 18:44
EMPOWERgmatRichC wrote:
Hi peachfuzz,

I think there's a typo in your work that has impacted ALL of your calculations:

The original 'symbol' in the prompt is....

a@b = a^2 - ab

It looks like your work is based on....

a@b = a^2 - 2ab

Your approach is perfect for this prompt though, so if you make the necessary adjustments to your work, you should get the correct answer.

GMAT assassins aren't born, they're made,
Rich

Whoops, you are correct! Thanks for catching my mistake.

I. x^2 - xy
can be true if x and y is equal to 1

II. (x^2)(y^2) - x(y^2)
can be true if x and y is equal to 1

III. -xy
will always equal a number that is not zero

B. I and II
Math Expert
Joined: 02 Sep 2009
Posts: 58382
Re: For all numbers a and b, the operation is defined by ab = a^2 - ab.  [#permalink]

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23 Mar 2015, 05:00
Bunuel wrote:
For all numbers a and b, the operation @ is defined by a@b = a^2 - ab. If xy ≠ 0, then which of the following can be equal to zero?

I. x@y

II. (xy)@y

III. x@(x + y)

A. II only
B. I and II only
C. I and III only
D. II and III only
E. All of the above

Kudos for a correct solution.

MAGOOSH OFFICIAL SOLUTION:
Attachment:

stranop_exp.png [ 43.62 KiB | Viewed 7714 times ]

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Re: For all numbers a and b, the operation is defined by ab = a^2 - ab.  [#permalink]

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11 Apr 2017, 06:49
Is that really a 700 question? Looks too straight

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Math Expert
Joined: 02 Sep 2009
Posts: 58382
For all numbers a and b, the operation is defined by ab = a^2 - ab.  [#permalink]

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11 Apr 2017, 07:05
mill wrote:
Is that really a 700 question? Looks too straight

Posted from my mobile device

Difficulty level (seen in tags) is calculated automatically based on the timer stats from the users who attempted the question.
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Re: For all numbers a and b, the operation is defined by ab = a^2 - ab.  [#permalink]

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11 Aug 2019, 02:55
I: x^2-xy= x(x-1)
II:(xy)^2-xy^2=xy^2(x-1)
III:x^2- x^2-xy
Only if X=1 the cases I & II can be zero.
Option B

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Re: For all numbers a and b, the operation is defined by ab = a^2 - ab.   [#permalink] 11 Aug 2019, 02:55
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# For all numbers a and b, the operation is defined by ab = a^2 - ab.

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