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Is a=b?

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Source: — Data Sufficiency |
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by neelgandham » Mon Oct 31, 2011 1:27 pm
rijul007 wrote:Is a=b?

Statement I:
(a+b)(1/a + 1/b) = 9

Statement II:
(a-4)^2 - (b-4)^2 = 0


p^q means p raised to the power q
IMO E
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by rijul007 » Mon Oct 31, 2011 2:04 pm
OA: A
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by GmatMathPro » Mon Oct 31, 2011 2:24 pm
Statement1. If a=b, then (a+b)(1/a+1/b) becomes (a+a)(1/a+1/a)=2a(2/a)=4 for all non-zero values of a and b. Thus, if (a+b)(1/a+1/b)=9, it must be that case that a does not equal b. SUFFICIENT.

Statement 2:

(a-4)^2-(b-4)^2=0
(a-4)^2=(b-4)^2

(a-4)=(b-4) or (a-4)=-(b-4)

a=b or a+b=8
So, it could be a=b or it could be any values of a and b that add to 8, like a=6 and b=2.
INSUFFICIENT.
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by GMATGuruNY » Mon Oct 31, 2011 3:16 pm
rijul007 wrote:Is a=b?

Statement I:
(a+b)(1/a + 1/b) = 9

Statement II:
(a-4)^2 - (b-4)^2 = 0

p^q means p raised to the power q
Another approach:

Statement 1: (a+b)(1/a + 1/b) = 9.
a/a + a/b + b/a + b/b = 9
a/b + b/a + 2 = 9
a/b + b/a = 7.
If a=b, then a/b + b/a = 2.
Thus, since a/b + b/a = 7, it is not possible that a=b.
SUFFICIENT.

Statement 2: (a-4)^2 - (b-4)^2 = 0.
Rephrased: |a-4| = |b-4|.
If a-4=b-4, then a=b.
If a-4=4-b, then a+b=8, in which case it is possible that a≠b.
INSUFFICIENT.

The correct answer is A.
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