GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 13 Dec 2019, 05:37 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # For all numbers a and b, the operation is defined by ab = a^2 - ab.

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 59720
For all numbers a and b, the operation is defined by ab = a^2 - ab.  [#permalink]

### Show Tags

2
11 00:00

Difficulty:   55% (hard)

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

### HideShow timer Statistics

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.

_________________
Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 9876
Location: Pune, India
Re: For all numbers a and b, the operation is defined by ab = a^2 - ab.  [#permalink]

### Show Tags

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)
_________________
Karishma
Veritas Prep GMAT Instructor

##### General Discussion
Senior Manager  B
Joined: 28 Feb 2014
Posts: 289
Location: United States
Concentration: Strategy, General Management
Re: For all numbers a and b, the operation is defined by ab = a^2 - ab.  [#permalink]

### Show Tags

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

EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15716
Location: United States (CA)
GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: For all numbers a and b, the operation is defined by ab = a^2 - ab.  [#permalink]

### Show Tags

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
_________________
Math Expert V
Joined: 02 Aug 2009
Posts: 8309
Re: For all numbers a and b, the operation is defined by ab = a^2 - ab.  [#permalink]

### Show Tags

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....
_________________
Senior Manager  B
Joined: 28 Feb 2014
Posts: 289
Location: United States
Concentration: Strategy, General Management
Re: For all numbers a and b, the operation is defined by ab = a^2 - ab.  [#permalink]

### Show Tags

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 V
Joined: 02 Sep 2009
Posts: 59720
Re: For all numbers a and b, the operation is defined by ab = a^2 - ab.  [#permalink]

### Show Tags

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 8016 times ]

_________________
Intern  Joined: 14 Dec 2016
Posts: 4
Re: For all numbers a and b, the operation is defined by ab = a^2 - ab.  [#permalink]

### Show Tags

Is that really a 700 question? Looks too straight

Posted from my mobile device
Math Expert V
Joined: 02 Sep 2009
Posts: 59720
For all numbers a and b, the operation is defined by ab = a^2 - ab.  [#permalink]

### Show Tags

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.
_________________
Senior Manager  G
Joined: 29 Jun 2019
Posts: 470
Re: For all numbers a and b, the operation is defined by ab = a^2 - ab.  [#permalink]

### Show Tags

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

Posted from my mobile device
_________________
Always waiting Re: For all numbers a and b, the operation is defined by ab = a^2 - ab.   [#permalink] 11 Aug 2019, 02:55
Display posts from previous: Sort by

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