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barakhaiev
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If a and b are positive, is (a^(-1) + b^(-1))^(-1) less than Updated on: 11 Oct 2013, 06:44
Originally posted by barakhaiev on 07 Nov 2009, 09:39.
Last edited by Bunuel on 11 Oct 2013, 06:44, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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63% (02:08) correct 37% (02:19) wrong based on 83 sessions

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If a and b are positive, is (a^(-1) + b^(-1))^(-1) less than (a^(-1)*b^(-1))^(-1)?

(1) a = 2b
(2) a + b > 1

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-a-and-b-are-positive-is-a-1-b-1-1-less-than-106509.html
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If a and b are positive, is (a^(-1) + b^(-1))^(-1) less than 07 Nov 2009, 09:46
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IMO B.

We want to find out if \(\frac{ab}{a+b} < ab\)

Statement 1) we do not know if a and b are integers. That means we do not know if a+b < 1 or > 1. Insufficient
Statement 2) This statement clearly tells us that a+b > 1. That means \(\frac{ab}{a+b} < ab\). Sufficient.
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If a and b are positive, is (a^(-1) + b^(-1))^(-1) less than 11 Oct 2013, 06:37
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barakhaiev
If a and b are positive, is \((a^-1 + b^-1)^-1\) less than \((a^-1b^-1)^-1\)?
(1) a = 2b
(2) a + b > 1

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
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I think that the formatting is messed up. What are those lines on top? Are they suppose to mean exponents?
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If a and b are positive, is (a^(-1) + b^(-1))^(-1) less than 11 Oct 2013, 06:46
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jlgdr
barakhaiev
If a and b are positive, is \((a^-1 + b^-1)^-1\) less than \((a^-1b^-1)^-1\)?
(1) a = 2b
(2) a + b > 1

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

I think that the formatting is messed up. What are those lines on top? Are they suppose to mean exponents?
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Question: is \((a^{-1}+b^{-1})^{-1}<(a^{-1}*b^{-1})^{-1}\)? --> \((\frac{1}{a}+\frac{1}{b})^{-1}<(\frac{1}{ab})^{-1}\) --> \(\frac{ab}{a+b}<ab\), as \(a\) and \(b\) are positive we can reduce by \(ab\) and finally question becomes: is \(a+b>1\)?

(1) a = 2b --> is \(3b>1\) --> is \(b>\frac{1}{3}\), we don't know that, hence this statement is not sufficient.
(2) a + b > 1, directly gives an answer. Sufficient.

Answer: B.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-a-and-b-are-positive-is-a-1-b-1-1-less-than-106509.html
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