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

 It is currently 18 Feb 2020, 04:07 ### 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 any numbers x and y, x<>y = 2x - y - xy. If x<>y = 0, then which

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 61269
For any numbers x and y, x<>y = 2x - y - xy. If x<>y = 0, then which  [#permalink]

### Show Tags

11 00:00

Difficulty:   55% (hard)

Question Stats: 65% (01:58) correct 35% (02:18) wrong based on 209 sessions

### HideShow timer Statistics

Tough and Tricky questions: Algebra.

For any numbers $$x$$ and $$y$$, $$x \diamond y = 2x - y - xy$$. If $$x \diamond y = 0$$, then which of the following CANNOT be $$y$$?

A. 3
B. 2
C. 0
D. $$-\frac{4}{3}$$
E. -2

Kudos for a correct solution.

_________________
Intern  Joined: 29 Sep 2014
Posts: 15
Re: For any numbers x and y, x<>y = 2x - y - xy. If x<>y = 0, then which  [#permalink]

### Show Tags

2
For y=2 the equation gives 1=0 which is impossible.

Manager  Joined: 10 Sep 2014
Posts: 96
Re: For any numbers x and y, x<>y = 2x - y - xy. If x<>y = 0, then which  [#permalink]

### Show Tags

A. plug in 3 for y to get 2x-3x-3=0 or -x=3. This could work
B. plug in 2 for y to get 2x-2-2x=0 or 0=2 and this is not true

SVP  Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1714
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: For any numbers x and y, x<>y = 2x - y - xy. If x<>y = 0, then which  [#permalink]

### Show Tags

3
1

Given that 2x - y - xy = 0

Bring "x" in terms of "y"

2x - xy = y

$$x = \frac{y}{2-y}$$

Denominator cannot be 0

y cannot be 2
Manager  Joined: 22 Sep 2012
Posts: 121
Concentration: Strategy, Technology
WE: Information Technology (Computer Software)
Re: For any numbers x and y, x<>y = 2x - y - xy. If x<>y = 0, then which  [#permalink]

### Show Tags

1

We can reduce 2x - y - xy = 0 to y = 2x/1+x

All numbers apart from y = 2 can be equated correctly.
Intern  Joined: 20 Jan 2013
Posts: 33
Re: For any numbers x and y, x<>y = 2x - y - xy. If x<>y = 0, then which  [#permalink]

### Show Tags

1
Given $$x \diamond y$$ = 2x - y - xy.
And $$x \diamond y$$ = 0

Let's Put this value in first equation. So, 2x-xy=y => x= y/2-y
Now we can check the given options one by one from the above equation.

a) y=3 => x = -3 Possible
b) y=2 => x= infinite, Y can not be 2.

hence Answer is B --> 2
Math Expert V
Joined: 02 Sep 2009
Posts: 61269
Re: For any numbers x and y, x<>y = 2x - y - xy. If x<>y = 0, then which  [#permalink]

### Show Tags

1
2
Bunuel wrote:

Tough and Tricky questions: Algebra.

For any numbers $$x$$ and $$y$$, $$x \diamond y = 2x - y - xy$$. If $$x \diamond y = 0$$, then which of the following CANNOT be $$y$$?

A. 3
B. 2
C. 0
D. $$-\frac{4}{3}$$
E. -2

Kudos for a correct solution.

Official Solution:

For any numbers $$x$$ and $$y$$, $$x \diamond y = 2x - y - xy$$. If $$x \diamond y = 0$$, then which of the following CANNOT be $$y$$?

A. 3
B. 2
C. 0
D. $$-\frac{4}{3}$$
E. -2

We must determine which of the answer choices cannot be a value of $$y$$.

If $$x \diamond y = 2x - y - xy$$ and $$x \diamond y = 0$$, we can combine equations to get: $$2x - y - xy = 0$$. Because the problem tells us that one value for $$y$$ is impossible, one answer choice will make the equation $$2x - y - xy = 0$$ false.

Plug in each answer choice and see which makes the equation false.

A. If $$y = 3$$, then $$2x - y - xy = 0$$ becomes $$2x - 3 - x(3) = 0$$. Combine like terms: $$-x - 3 = 0$$, so $$x = -3$$. Because $$x$$ is a variable, it can be equal to any quantity. Therefore, this equation is not false.

B. If $$y = 2$$, then $$2x - 2 - x(2) = 0$$. The $$x$$ terms cancel, leaving $$-2 = 0$$. This is false, so B is correct. Double-check by making sure that no other answer yields a false equation.

C. If $$y = 0$$, then $$2x - 0 - x(0) = 0$$. This simplifies to $$2x = 0$$, which is not false.

D. If $$y = -\frac{4}{3}$$ then $$2x - (-\frac{4}{3}) - x(-\frac{4}{3}) = 0$$. Combine like terms: $$\frac{10}{3}x + \frac{4}{3} = 0$$. Isolate the $$x$$ term: $$\frac{10}{3}x = -\frac{4}{3}$$, so $$x = -\frac{2}{5}$$. This is not false.

E. If $$y = -2$$, then $$2x - (-2) - x(-2) = 0$$. Combine like terms: $$4x +2 = 0$$. Isolate the $$x$$ term: $$4x = -2$$, so $$x = -\frac{1}{2}$$. This is not false, so only choice B yields a false equation.

Choice B is the correct answer.

Alternatively, we can solve this problem using algebra. Recall that a value can be impossible for a variable in two ways: if the value of the variable causes a division by 0 or if the value forces the equation to look for the square root of a negative number. Since there are no exponents or roots in this equation, the answer will likely involve dividing by zero. If plugging in a certain value for $$y$$ causes a division by zero, we should look for $$y$$ in the denominator of a fraction. Solving the equation for $$x$$ may give us a fraction in terms of $$y$$.

First factor out the $$x$$ to get $$x(2 - y) - y = 0$$.

Add $$y$$ to both sides: $$x(2 - y) = y$$.

Divide both sides by $$2 - y$$ to get $$x = \frac{y}{2-y}$$.

If $$y = 2$$, the denominator becomes $$2 - 2 = 0$$. Any value that makes a denominator equal to 0 cannot be a valid solution to an equation because dividing by 0 is undefined. Therefore, $$y$$ cannot be equal to 2.

_________________
Director  G
Joined: 23 Jan 2013
Posts: 514
Schools: Cambridge'16
For any numbers x and y, x<>y = 2x - y - xy. If x<>y = 0, then which  [#permalink]

### Show Tags

Means that

2x-y-xy=0
x(2-y)-y=0
x(2-y)=y
so, test every option

A) x(2-3)=3 is possible when x=-3
B) x(2-2)=2 is not possible in any x
C) x(2-0)=0 is possible when x=0
D) x(2--4/3)=-4/3 is possible when x=-4/3:10/3
E) x(2--2)=-2 is possible when x=-1/2

B
Non-Human User Joined: 09 Sep 2013
Posts: 14075
Re: For any numbers x and y, x<>y = 2x - y - xy. If x<>y = 0, then which  [#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 any numbers x and y, x<>y = 2x - y - xy. If x<>y = 0, then which   [#permalink] 23 Nov 2019, 00:26
Display posts from previous: Sort by

# For any numbers x and y, x<>y = 2x - y - xy. If x<>y = 0, then which  