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# Does (x + y)² + (x – y)² = 170?

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Intern
Joined: 28 Apr 2014
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Does (x + y)² + (x – y)² = 170?  [#permalink]

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11 Jun 2015, 23:07
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Difficulty:

25% (medium)

Question Stats:

74% (01:20) correct 26% (01:29) wrong based on 101 sessions

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Does (x + y)^2 + (x – y)^2 = 170?

(1) x^2 + y^2 = 85
(2) x = y + 1
Intern
Joined: 28 Jan 2013
Posts: 31
Location: United States
GPA: 3.1
WE: Information Technology (Consulting)
Re: Does (x + y)² + (x – y)² = 170?  [#permalink]

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11 Jun 2015, 23:27
zahraf
Does (x + y)² + (x – y)² = 170?

(1) x² + y² = 85

Either x=7,y=6 or x=6,y=7 are the only values that satisfy the above equation.
case i) x=7,y=6
value of (x + y)² + (x – y)² will be 170

case ii) x=6,y=7
value of (x + y)² + (x – y)² will be 170

Sufficient

(2) x = y + 1
for this you can't get the exact values of x and y.

Say
X=7,Y=6
then (x + y)² + (x – y)² will be 170
X=5,Y=4
then (x + y)² + (x – y)² will be 82
so clearly statement 2 is Insufficient

Ans : A

Regards,
Manoj Reddy
Please press +1 kudos if you appreciate this post !!
Math Expert
Joined: 02 Sep 2009
Posts: 49990
Re: Does (x + y)² + (x – y)² = 170?  [#permalink]

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12 Jun 2015, 01:57
1
zahraf wrote:
Does (x + y)^2 + (x – y)^2 = 170?

(1) x^2 + y^2 = 85
(2) x = y + 1

Does (x + y)^2 + (x – y)^2 = 170?

Does x^2 + 2xy + y^2 + x^2 - 2xy + y^2 = 170?
Does 2x^2 + 2y^2 = 170?
Does x^2 + y^2 = 85?

(1) x^2 + y^2 = 85. Directly answers the question. Sufficient.

(2) x = y + 1. If x = 1 and y = 0, then the answer is NO but if x = 7 and y = 6, then the answer is YES. Not sufficient.

Hope it's clear.
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Math Expert
Joined: 02 Sep 2009
Posts: 49990
Re: Does (x + y)² + (x – y)² = 170?  [#permalink]

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12 Jun 2015, 02:04
1
ManojReddy wrote:
zahraf
Does (x + y)² + (x – y)² = 170?

(1) x² + y² = 85

Either x=7,y=6 or x=6,y=7 are the only values that satisfy the above equation.
case i) x=7,y=6
value of (x + y)² + (x – y)² will be 170

case ii) x=6,y=7
value of (x + y)² + (x – y)² will be 170

Sufficient

(2) x = y + 1
for this you can't get the exact values of x and y.

Say
X=7,Y=6
then (x + y)² + (x – y)² will be 170
X=5,Y=4
then (x + y)² + (x – y)² will be 82
so clearly statement 2 is Insufficient

Ans : A

Regards,
Manoj Reddy
Please press +1 kudos if you appreciate this post !!

Red text above is not correct.

We are not told that x and y are integers, so x^2 + y^2 = 85 will have infinite number of solutions.

Next, even if we were told that x and y are integers, there still would be more solutions (16 integer solutions):
x = ±9, y = ±2;
x = ±7, y = ±6;
x = ±6, y = ±7;
x = ±2, y = ±9.

Hope it helps.
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Posts: 8446
Re: Does (x + y)² + (x – y)² = 170?  [#permalink]

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31 Oct 2017, 16:16
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Re: Does (x + y)² + (x – y)² = 170? &nbs [#permalink] 31 Oct 2017, 16:16
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