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# What is the value of x^2 − y^2 ? (1) (x - y)^2 = 9 (2) x + y = 6

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Joined: 01 Sep 2010
Posts: 3292
What is the value of x^2 − y^2 ? (1) (x - y)^2 = 9 (2) x + y = 6  [#permalink]

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27 Jul 2017, 07:09
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Top Contributor
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Difficulty:

25% (medium)

Question Stats:

70% (01:17) correct 30% (01:25) wrong based on 400 sessions

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What is the value of $$x^2 - y^2$$ ?

(1) $$(x - y)^2 = 9$$

(2) x + y = 6

(DS03308)

_________________
Math Expert
Joined: 02 Aug 2009
Posts: 7099
Re: What is the value of x^2 − y^2 ? (1) (x - y)^2 = 9 (2) x + y = 6  [#permalink]

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27 Jul 2017, 08:14
2
1
carcass wrote:
What is the value of $$x^2 - y^2$$ ?

(1) $$(x - y)^2 = 9$$

(2) x + y = 6

$$x^2-y^2=(x+y)(x-y)$$

STATEMENTS..

(1) $$(x - y)^2 = 9$$
x-y= 3..
x-y=-3..
various combinations of x and y possible fitting in any of two above
insuff

(2) x + y = 6
we do not know what is x-y
insuff

combined..
we know x+y=6..
but x-y can be 3, then ans is 18
OR x-y can be -3 ans will be -18

insuff

E
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: What is the value of x^2 − y^2 ? (1) (x - y)^2 = 9 (2) x + y = 6  [#permalink]

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06 Aug 2017, 06:50
1
lets consider both case 1 and 2

x=6-y

(6-y-y)^2=9
6-2y=3 or -3
we can have two values of y and x

so, not sufficient

e
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Joined: 08 May 2018
Posts: 25
Re: What is the value of x^2 − y^2 ? (1) (x - y)^2 = 9 (2) x + y = 6  [#permalink]

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31 Jul 2018, 07:03
What is the value of $$x^2 - y^2$$?

(1) $$(x-y)^2=9$$
(2) $$x+y=6$$
Director
Joined: 31 Oct 2013
Posts: 852
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: What is the value of x^2 − y^2 ? (1) (x - y)^2 = 9 (2) x + y = 6  [#permalink]

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31 Jul 2018, 07:11
throw123 wrote:
What is the value of $$x^2 - y^2$$?

(1) $$(x-y)^2=9$$
(2) $$x+y=6$$

$$x^2 - y^2 = (x+y) (x - y)$$

Statement 1 :

$$(x-y)^2 = 9$$

x - y = +3 or -3

At the same time we don't know about x-y

NOT sufficient.

Statement 2 :

x + y = 6.

No information regarding x - y .Not sufficient.

1+ 2:

As we have 2 values for x - y , it's not possible to find out any specific value of $$x^2 - y^2$$

Math Expert
Joined: 02 Sep 2009
Posts: 51098
Re: What is the value of x^2 − y^2 ? (1) (x - y)^2 = 9 (2) x + y = 6  [#permalink]

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31 Jul 2018, 08:41
throw123 wrote:
What is the value of $$x^2 - y^2$$?

(1) $$(x-y)^2=9$$
(2) $$x+y=6$$

Merging topics. Please check the discussion above.
_________________
Re: What is the value of x^2 − y^2 ? (1) (x - y)^2 = 9 (2) x + y = 6 &nbs [#permalink] 31 Jul 2018, 08:41
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