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Does a^2 + b^2 = 2ab?

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Does a^2 + b^2 = 2ab? [#permalink]

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New post 19 Sep 2017, 01:22
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

63% (01:06) correct 37% (01:21) wrong based on 29 sessions

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Kudos [?]: 128929 [0], given: 12183

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Joined: 18 Aug 2016
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Does a^2 + b^2 = 2ab? [#permalink]

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New post 19 Sep 2017, 01:30
Bunuel wrote:
Does a^2 + b^2 = 2ab?

(1) a + b = 3
(2) ab > 0


a^2 + b^2 = 2ab
a^2 + b^2 - 2ab = 0
(a-b)^2 = 0
Is a equal to b?

(1) a,b can be 3/2,3/2 or 2,1..not sufficient

(2) ab can be equal (1,1) and cannot be equal (3,2) same sign
not sufficient

on combining 3/2,3/2 or 2,1 give different answers

E

P.S. Second attempt
_________________

We must try to achieve the best within us

Thanks
Luckisnoexcuse


Last edited by Luckisnoexcuse on 19 Sep 2017, 03:48, edited 1 time in total.

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Does a^2 + b^2 = 2ab? [#permalink]

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New post 19 Sep 2017, 02:46
Luckisnoexcuse wrote:
Bunuel wrote:
Does a^2 + b^2 = 2ab?

(1) a + b = 3
(2) ab > 0


a^2 + b^2 = 2ab
a^2 + b^2 - 2ab = 0
(a-b)^2 = 0
Is a equal to b?

(1) a is not equal to b..sufficient

(2) ab can be equal (1,1) and cannot be equal (3,2)
not sufficient

A



The ques basically asks whether a=b..

with 1) a+b=3, we can have it as yes ( a=1.5 and b=1.5) or no (a=1 and b=2)
So A can not be the answer.

with 2, both a and b have the same sign. Not sufficient.

With 1 and 2, we know that a+b=3 and a & b are of the same sign.

a = 1 and b=2 (same sign) we get a NO
a=1.5 and b=1.5 (same sign) we get a YES.

i think the answer should be E.

chetan2u, any help would be appreciated.

Kudos [?]: 2 [0], given: 8

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Re: Does a^2 + b^2 = 2ab? [#permalink]

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New post 23 Sep 2017, 22:04
Bunuel wrote:
Does a^2 + b^2 = 2ab?

(1) a + b = 3
(2) ab > 0



I will go with E

because ...
(1)
(a+b)^2 = a^2 + 2ab + b^2
9 = a^2 + b^2 + 2ab

different values will satisfy this equation..
not sufficient

(2) ab > 0
so what? not sufficient

(1) + (2)
even 2 statements together do not help much...

Kudos [?]: 14 [0], given: 413

Re: Does a^2 + b^2 = 2ab?   [#permalink] 23 Sep 2017, 22:04
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