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x+y=4

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x+y=4 [#permalink] New post 08 Sep 2018, 22:35
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Question Stats:

92% (00:22) correct 7% (01:06) wrong based on 14 sessions
\(x+y=4\)

\(xy=0\)

Quantity A
Quantity B
\(x\)
\(y\)


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Kudos for R.A.E
[Reveal] Spoiler: OA

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Re: x+y=4 [#permalink] New post 09 Sep 2018, 07:01
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Expert's post
Carcass wrote:
\(x+y=4\)

\(xy=0\)

Quantity A
Quantity B
\(x\)
\(y\)


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

Kudos for R.A.E


GIVEN: x + y = 4 and xy = 0

If xy = 0, then EITHER x = 0 OR y = 0
Let's examine each possible case:

Case i) if x = 0, then y = 4 (since we're also told that x + y = 4)
Case ii) if y = 0, then x = 4 (since we're also told that x + y = 4)

In case i, Quantity A is greater than Quantity B
In case ii, Quantity B is greater than Quantity A

Answer: D

Cheers,
Brent
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Re: x+y=4 [#permalink] New post 09 Sep 2018, 09:11
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if X+Y = 4 & XY = 0

We can write as

= (X-Y)^2

= X^2+Y^2-2XY

= (X+Y)^2-4XY ( Bifurcating the equation)

= 4^2-4*0

= 16

THEREFORE

X-Y = 16^0.5

(Taking square root of 16)

X-Y = (+/-) 4


Now we have

X+Y = 4 .....1

X-Y = 4 .....2

On solving the equation 1 & 2 we get as follows:

X = 4

Y = 0

AND

X-Y = 4 .....2

X-Y = -4 ...4

On solving the equation 3 & 4 we get as follows:

X = 0

Y = 4


Since both X & Y can take both values 0 and 4 which is contradictory statements regarding the large value among X & Y.


Hence the answer is "D"


HENCE PROVED
Re: x+y=4   [#permalink] 09 Sep 2018, 09:11
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