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# What is the value of (a+b)^2?

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Manager
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What is the value of (a+b)^2? [#permalink]

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24 Dec 2012, 18:59
00:00

Difficulty:

15% (low)

Question Stats:

73% (01:52) correct 27% (00:59) wrong based on 120 sessions

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What is the value of (a+b)^2?

(1) ab = 0
(2) (a-b)^2 = 36
[Reveal] Spoiler: OA

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Re: What is the value of (a+b)^2? [#permalink]

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25 Dec 2012, 05:02
megafan wrote:
What is the value of (a+b)^2?

(1) ab = 0
(2) (a-b)^2 = 36

Each statement alone is clearly insufficient. When we take the statements together we have: ab=0 and a^2-2ab+b^2=36, thus a^2+b^2=36 --> (a+b)^2=a^2+2ab+b^2=36+0=36. Sufficient.

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Re: What is the value of (a+b)^2? [#permalink]

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14 May 2015, 04:40
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Re: What is the value of (a+b)^2? [#permalink]

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14 May 2015, 22:41
Hi All,

This question can be solved with Algebra (and recognizing Classic Quadratics) or by TESTing VALUES.

We're asked for the value of (A+B)^2

Fact 1: AB = 0

This means that either A or B or Both = 0

IF...
A = 0
B = 0
(0+0)^2 = 0

IF....
A = 1
B = 0
(1+0)^2 = 1
Fact 1 is INSUFFICIENT

Fact 2: (A-B)^2 = 36

This ultimately means that (A-B) = 6 or -6

IF.....
A = 6
B = 0
(6+0)^2 = 36

IF....
A = 7
B = 1
(7+1)^2 = 64
Fact 2 is INSUFFICIENT

Combined, we know....
A or B or Both = 0
(A-B) = 6 or -6

IF....
A = 0
B = 6 OR -6
(0+6)^2 = (0-6)^2 = 36

IF....
B = 0
A = 6 OR -6
(0+6)^2 = (0-6)^2 = 36

Combined, SUFFICIENT

[Reveal] Spoiler:
C

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Re: What is the value of (a+b)^2? [#permalink]

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15 May 2015, 09:46
$$(a+b)^2= a^2+b^2+2ab$$

St1
ab=0
=> either a=0 or b=0 or both.
=> $$(a+b)^2= a^2+b^2$$
Since we cant determine this value. Insufficient

St2
($$a-b)^2=36$$
=>$$a^2+b^2-2ab=36$$
Insufficient

St1+St2
since ab=0, $$(a-b)^2=a^2+b^2=36 = (a+b)^2$$
Sufficient

Re: What is the value of (a+b)^2?   [#permalink] 15 May 2015, 09:46
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