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# Does (x + y)^2 + (x - y)^2 = 170?

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Math Expert
Joined: 02 Sep 2009
Posts: 52295
Does (x + y)^2 + (x - y)^2 = 170?  [#permalink]

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08 Feb 2018, 05:30
00:00

Difficulty:

35% (medium)

Question Stats:

83% (01:48) correct 17% (02:24) wrong based on 56 sessions

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Does (x + y)^2 + (x - y)^2 = 170?

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

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Joined: 24 Jun 2013
Posts: 132
Location: India
Schools: ISB '20
Re: Does (x + y)^2 + (x - y)^2 = 170?  [#permalink]

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08 Feb 2018, 06:34
1
Reducing the question we get : is x2+y2= 85? ( +2xy-2xy cancel out each other and 170/2 = 85)

st1 : directly given >> suff
st2: x=y+1>> now given that x and y are consecutive numbers , so square of consecutive number summing up to 85 is 6 and 7 any other value ans is no >> insuff

A
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Re: Does (x + y)^2 + (x - y)^2 = 170?  [#permalink]

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08 Feb 2018, 20:22
Does (x + y)^2 + (x - y)^2 = 170?

(1) x^2 + y^2= 85
From the question stem, x^2+y^2+2xy+x^2+y^2-2xy=170
2xy cancels out on both side, which results in x^2+y^2 = 85 which matches with option A

Sufficient

(2) x = y + 1
There are more than 1 options. Hence insufficient

Ans: A
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Re: Does (x + y)^2 + (x - y)^2 = 170? &nbs [#permalink] 08 Feb 2018, 20:22
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