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

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

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New post 19 Mar 2015, 06:31
2
11
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

66% (02:08) correct 34% (02:21) wrong based on 291 sessions

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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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New post 19 Mar 2015, 21:42
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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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Re: For all numbers a and b, the operation is defined by ab = a^2 - ab.  [#permalink]

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New post 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

Answer: D
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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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New post 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.

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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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New post 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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New post 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
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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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New post 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
stranop_exp.png [ 43.62 KiB | Viewed 8016 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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New post 11 Apr 2017, 06:49
Is that really a 700 question? Looks too straight

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

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New post 11 Apr 2017, 07:05
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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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New post 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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