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(x+5)^2 - (y-3)^2 = 0 and x +y =2

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whollymoses
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(x+5)^2 - (y-3)^2 = 0 and x +y =2 [#permalink] New post   Updated on: 14 Oct 2020, 13:13
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\((x+5)^2 - (y-3)^2=0\)

\(x + y = 2\)

Quantity A
Quantity B
\(x-\)y
\(0\)


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
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Official Answer
B

Originally posted by whollymoses on 14 Oct 2020, 11:05.
Last edited by Carcass on 14 Oct 2020, 13:13, edited 1 time in total.
Edited by Carcass
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B
kapil1
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Re: (x+5)^2 - (y-3)^2 = 0 and x +y =2 [#permalink] New post   17 Oct 2020, 06:18
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Quote:
\((x+5)^2−(y−3)^2\)=0

Step 1: Understanding the question
The equation is in the form of \(a^2 - b^2\) = (a+b) (a-b)

Step 2: Calculation
(x+5 + y−3) (x+5-y +3) =0

(x+y+2) (x-y+8) = 0

(2+2) (x-y+8) = 0

4(x-y+8) = 0

hence, x-y = -8

B is correct
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Re: (x+5)^2 - (y-3)^2 = 0 and x +y =2 [#permalink] New post   14 Oct 2020, 13:14
Expert Reply
Please Sir, see how to format a QCQ properly and the use of the timer. It will take one minutes to post a question in the right manner

https://gre.myprepclub.com/forum/how-to-po ... 12752.html

Thank you for your collaboration

Regards
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Re: (x+5)^2 - (y-3)^2 = 0 and x +y =2 [#permalink] New post   14 Oct 2020, 13:56
1
\((X+5)^2-(y-3)^2=0\)

\(X+y=2\)

From eqn 2:-X=2-y substitute this in eqn 1

\((2-y+5)^2-(y-3)^2=0\)

\((7-y)^2 -(y-3)^2\)

\((7-y)^2=y^2-14y+49\)

\((Y-3) ^2=y^2-6y+9\)

Subtracting the two expression above

\(Y^2-14y+49-[y^2 -6y -9]=0\)

We got \(-8y+40=0\)

\(Y=5\)

Then \(x =2-5\)

\(X=-3\)

QtyA is x-y which equal -3-5=-8

QTY B 0

Hence ans is B
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Re: (x+5)^2 - (y-3)^2 = 0 and x +y =2 [#permalink] New post   15 Oct 2020, 14:06
Bruteforcing and just solving seems pretty time consuming -- Is there any other method besides foiling and substituting to solve?
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Re: (x+5)^2 - (y-3)^2 = 0 and x +y =2 [#permalink] New post   22 Oct 2024, 04:01
Hello from the GRE Prep Club BumpBot!

Thanks to another GRE Prep 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).

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Re: (x+5)^2 - (y-3)^2 = 0 and x +y =2 [#permalink]
22 Oct 2024, 04:01
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