GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 19 Jan 2020, 12:50 ### 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 real numbers x and y, let x# y = (xy)^2 − x + y^2. What is the

Author Message
TAGS:

### Hide Tags

Senior RC Moderator V
Joined: 02 Nov 2016
Posts: 4854
GPA: 3.39
For all real numbers x and y, let x# y = (xy)^2 − x + y^2. What is the  [#permalink]

### Show Tags

1
4 00:00

Difficulty:   5% (low)

Question Stats: 90% (01:19) correct 10% (01:50) wrong based on 123 sessions

### HideShow timer Statistics

For all real numbers $$x$$ and $$y$$, let x#y = $$(xy)^2 − x + y^2$$ . What is the value of y that makes x # y equal to $$–x$$ for all values of $$x$$ ?

(A) 0
(B) 2
(C) 5
(D) 7
(E) 10

Source: Nova GMAT
Difficulty Level: 500

_________________
Retired Moderator P
Joined: 22 Aug 2013
Posts: 1403
Location: India
Re: For all real numbers x and y, let x# y = (xy)^2 − x + y^2. What is the  [#permalink]

### Show Tags

We have to make x#y = -x
or (x^2)(y^2) -x + y^2 = -x
y^2 (x^2 + 1) = 0

This equation will obviously be true for all values of x if y^2 = 0 or if y=0

Hence A
Senior PS Moderator V
Joined: 26 Feb 2016
Posts: 3295
Location: India
GPA: 3.12
Re: For all real numbers x and y, let x# y = (xy)^2 − x + y^2. What is the  [#permalink]

### Show Tags

2
The only possibility for the equation,
when x#y = $$(xy)^2 − x + y^2$$ = -x is when $$(xy)^2 + y^2 = 0$$.
Only one possibility can give us a 0 for the expression at all possible values of x(y=0)
If y =0, the expression will always yield a zero and hence the value of x#y will always be -x

Therefore, Option A is the correct answer.
_________________
You've got what it takes, but it will take everything you've got
Intern  Joined: 17 Feb 2018
Posts: 1
Re: For all real numbers x and y, let x# y = (xy)^2 − x + y^2. What is the  [#permalink]

### Show Tags

for all numbers x and y ,let x club y be defined as x club y=x^2 -2xy +y^2 what is the value of (2 club 4) club 8?
Intern  Joined: 31 Jan 2018
Posts: 15
Re: For all real numbers x and y, let x# y = (xy)^2 − x + y^2. What is the  [#permalink]

### Show Tags

(xy)^2-x+y^2=-x
So (y^2)(x^2+1)=0
As x^2+1 cannot be zero.
So y=0
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4214
Re: For all real numbers x and y, let x# y = (xy)^2 − x + y^2. What is the  [#permalink]

### Show Tags

Top Contributor
For all real numbers x and y, let x# y = (xy)^2 − x + y^2 . What is the value of y that makes x # y equal to –x for all values of x ?

(A) 0
(B) 2
(C) 5
(D) 7
(E) 10

APPROACH #1
We want the following equation to hold true: x # y = –x
Replace x # y with its equivalent to get: (xy)² − x + y² = -x
Add x to both sides to get: (xy)² + y² = 0
Simplify (xy)² to get: x²y² + y² = 0
Factor out the y² to get: y²(x² + 1) = 0
So, the equation will hold true when EITHER y² = 0 OR x² + 1 = 0
If y² = 0, then y =0

Cheers,
Brent
_________________
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4214
Re: For all real numbers x and y, let x# y = (xy)^2 − x + y^2. What is the  [#permalink]

### Show Tags

1
Top Contributor
For all real numbers x and y, let x# y = (xy)^2 − x + y^2 . What is the value of y that makes x # y equal to –x for all values of x ?

(A) 0
(B) 2
(C) 5
(D) 7
(E) 10

APPROACH #2 - Test the answer choices

A) 0
Take x#y = (xy)² − x + y², and replace y with 0
We get: [(x)(0)]² − x + 0² = ² − x + 0
= -x
So, when y = 0, x#y = -x
PERFECT!

Cheers,
Brent
_________________
Non-Human User Joined: 09 Sep 2013
Posts: 13983
Re: For all real numbers x and y, let x# y = (xy)^2 − x + y^2. What is the  [#permalink]

### Show Tags

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________ Re: For all real numbers x and y, let x# y = (xy)^2 − x + y^2. What is the   [#permalink] 24 Aug 2019, 14:15
Display posts from previous: Sort by

# For all real numbers x and y, let x# y = (xy)^2 − x + y^2. What is the   