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

 It is currently 07 Dec 2019, 17:39

### 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

# What is the value of x + y? (1) (4x^2 - 4y^2)/(2(x+y)) = 2x - 2y

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 59588
What is the value of x + y? (1) (4x^2 - 4y^2)/(2(x+y)) = 2x - 2y  [#permalink]

### Show Tags

14 Oct 2019, 02:42
00:00

Difficulty:

35% (medium)

Question Stats:

73% (01:37) correct 27% (01:34) wrong based on 41 sessions

### HideShow timer Statistics

Competition Mode Question

What is the value of x + y?

(1) $$\frac{4x^2−4y^2}{2(x+y)}=2x - 2y$$

(2) $$3x + 2y = 24$$

_________________
Senior Manager
Joined: 01 Mar 2019
Posts: 332
Location: India
Concentration: Strategy, Social Entrepreneurship
Schools: Ross '22, ISB '20, NUS '20
GPA: 4
Re: What is the value of x + y? (1) (4x^2 - 4y^2)/(2(x+y)) = 2x - 2y  [#permalink]

### Show Tags

14 Oct 2019, 03:15
1
1) both sides get cancelled and results in zero.....insuff
2) as we are aware of limitations of x,y whether int/dec/natural numbers the equation satisfies many values of x,y .......insufff

Both combined also insuff

OA:E
Senior Manager
Joined: 10 Apr 2018
Posts: 281
Location: India
Concentration: General Management, Operations
GMAT 1: 680 Q48 V34
GPA: 3.3
Re: What is the value of x + y? (1) (4x^2 - 4y^2)/(2(x+y)) = 2x - 2y  [#permalink]

### Show Tags

14 Oct 2019, 03:34
1
(1) As LHS=RHS, simplifying the expression gives no new information.
Thus, insufficient.

(2) Not enough information available.
Thus, insufficient.

From (1) and (2), we don't have enough data.
Thus, insufficient.

Therefore, the answer is option E.
Senior Manager
Joined: 07 Mar 2019
Posts: 434
Location: India
GMAT 1: 580 Q43 V27
WE: Sales (Energy and Utilities)
Re: What is the value of x + y? (1) (4x^2 - 4y^2)/(2(x+y)) = 2x - 2y  [#permalink]

### Show Tags

14 Oct 2019, 03:51
1
What is the value of x + y?

(1) $$\frac{4x^2 − 4y^2}{2(x + y)}$$ = 2x − 2y

$$\frac{(2x − 2y) * (2x + 2y)}{2(x + y)}$$ = 2x − 2y

2x - 2y = 2x − 2y

Many values of x and y would satisfy the condition. Hence

INSUFFICIENT.

(2) 3x+2y=24

(0, 12), (2, 9), (4, 6) and many other values including decimals satisfy the conditions. So,

INSUFFICIENT.

Together 1 and 2 there's nothing new so,

INSUFFICIENT.

_________________
Ephemeral Epiphany..!

GMATPREP1 590(Q48,V23) March 6, 2019
GMATPREP2 610(Q44,V29) June 10, 2019
GMATPREPSoft1 680(Q48,V35) June 26, 2019
Director
Joined: 18 May 2019
Posts: 528
Re: What is the value of x + y? (1) (4x^2 - 4y^2)/(2(x+y)) = 2x - 2y  [#permalink]

### Show Tags

14 Oct 2019, 04:18
We are to determine x+y

Statement 1: (4x^2-4y^2)/(2(x+y))=2x-2y
(x+y)(x-y)=(x+y)(x-y)
since LHS=RHS of the equation above, x+y has an infinite possibilities which satisfy the given equation. Statement 1 is therefore insufficient.

Statement 2: 3x+2y=24
x+y=(24-x)/2
from the above, x+y depends on the value of x, and x can assume any number, implying x+y has infinitely many possibilities. Statement 2 is not sufficient.

1+2
Still insufficient because there are infinite possibilities for x+y even when both statements are combined. We are unable to narrow the value of x+y to unique values.

The answer is E in my view.
Director
Joined: 24 Nov 2016
Posts: 927
Location: United States
What is the value of x + y? (1) (4x^2 - 4y^2)/(2(x+y)) = 2x - 2y  [#permalink]

### Show Tags

Updated on: 15 Oct 2019, 04:23
Quote:
What is the value of x + y?

(1) $$\frac{4x^2−4y^2}{2(x+y)}=2x−2y$$
(2) 3x+2y=24

(1) $$\frac{4x^2−4y^2}{2(x+y)}=2x−2y…\frac{4(x+y)(x-y)}{2(x+y)}=2(x-y)…x-y=x-y…(x,y)=anything$$: insufic.

(2) $$3x+2y=24…3x=24-2y…x=\frac{24-2y}{3}$$: insufic.

(1&2): $$(x,y)=anything$$, insufic.
$$y=3…x=\frac{24-2y}{3}=\frac{24-6}{3}=6…x+y=9$$
$$y=6…x=\frac{24-2y}{3}=\frac{24-12}{3}=4…x+y=10$$

Originally posted by exc4libur on 14 Oct 2019, 04:38.
Last edited by exc4libur on 15 Oct 2019, 04:23, edited 1 time in total.
Senior Manager
Joined: 25 Jul 2018
Posts: 386
Re: What is the value of x + y? (1) (4x^2 - 4y^2)/(2(x+y)) = 2x - 2y  [#permalink]

### Show Tags

14 Oct 2019, 05:09
1
What is the value of x + y?

(Statement1) $$\frac{4x^{2}−4y^{2}}{2(x+y)}=2x−2y$$
--> $$\frac{4(x-y)(x+y)}{2(x+y)}=2(x-y)$$
x+y≠0 --> $$(x-y)*(\frac{x+y}{x+y}-1)$$=0
x=y, $$\frac{0}{x+y}$$=0

--> x+y=2x or x+y=2y
NO info about what x and y are.
Insufficient

(Statement2) 3x+2y=24
if x=8 and y=0--> 3*8+2*0=24
x+y=8

if if x=6 and y=3--> 3*6+2*3=24
x+y=9
Insufficient

Taken together 1&2, there are more than one value of (x+y)
Insufficient

Senior Manager
Joined: 22 Feb 2018
Posts: 317
Re: What is the value of x + y? (1) (4x^2 - 4y^2)/(2(x+y)) = 2x - 2y  [#permalink]

### Show Tags

14 Oct 2019, 07:23
1
What is the value of x + y?

(1) 4x^2−4y^2/2(x+y)=2x−2y
4 (x^2−y^2/2(x+y)=2(x−y)
4 (x^2−y^2)=4 (x^2−y^2)
LHS = RHS
Infinite values of x and y can satisfy the equation. Hence, insufficient.

(2) 3x+2y=24
x=2 and y = 9 or x=4 and y = 6
Hence, x+ y = 11/10.... Hence, insufficient.

1) and 2) There will be multiple number of x and y, hence unique value of x and y can not be obtained. Insufficient

Imo. E.
_________________
Thanks in the forum can be expressed by hitting KUDOS!!!
Re: What is the value of x + y? (1) (4x^2 - 4y^2)/(2(x+y)) = 2x - 2y   [#permalink] 14 Oct 2019, 07:23
Display posts from previous: Sort by