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

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

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New post 14 Oct 2019, 02:42
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A
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D
E

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  35% (medium)

Question Stats:

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

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Re: What is the value of x + y? (1) (4x^2 - 4y^2)/(2(x+y)) = 2x - 2y  [#permalink]

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New post 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
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Re: What is the value of x + y? (1) (4x^2 - 4y^2)/(2(x+y)) = 2x - 2y  [#permalink]

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New post 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.
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Re: What is the value of x + y? (1) (4x^2 - 4y^2)/(2(x+y)) = 2x - 2y  [#permalink]

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New post 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.

IMO Answer E.
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Re: What is the value of x + y? (1) (4x^2 - 4y^2)/(2(x+y)) = 2x - 2y  [#permalink]

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New post 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.
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What is the value of x + y? (1) (4x^2 - 4y^2)/(2(x+y)) = 2x - 2y  [#permalink]

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New post 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.
\(y=3…x=\frac{24-2y}{3}=\frac{24-6}{3}=6…x+y=9\)
\(y=6…x=\frac{24-2y}{3}=\frac{24-12}{3}=4…x+y=10\)

Answer (E)

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.
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Re: What is the value of x + y? (1) (4x^2 - 4y^2)/(2(x+y)) = 2x - 2y  [#permalink]

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New post 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

The answer is E.
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Re: What is the value of x + y? (1) (4x^2 - 4y^2)/(2(x+y)) = 2x - 2y  [#permalink]

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New post 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.
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Re: What is the value of x + y? (1) (4x^2 - 4y^2)/(2(x+y)) = 2x - 2y   [#permalink] 14 Oct 2019, 07:23
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