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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
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64% (01:33) correct 36% (01:33) wrong based on 225 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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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.

GMAT assassins aren't born, they're made,
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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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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, 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 4281 times ]

_________________

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

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New post 17 Jun 2018, 15:15
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Re: For all numbers a and b, the operation is defined by ab = a^2 - ab.   [#permalink] 17 Jun 2018, 15:15
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