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

Statement(1) ALONE is sufficient, but statement (2) alone is not sufficient.

Statement(2) ALONE is sufficient, but statement (1) alone is not sufficient.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are NOT sufficient.

B

## If a and b are positive...

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- Marty Murray
- Legendary Member
**Posts:**2073**Joined:**03 Feb 2014**Location:**New York City Metro Area and Worldwide Online**Thanked**: 955 times**Followed by:**136 members**GMAT Score:**800

I see a big clue in Statement 2. If a + b > 1 is one of the Statements, then maybe whether a + b > 1 is the case makes a difference. So I am going to try numbers that are integers and fractions.ssyohee wrote:If a and b are positive, is (aâ�»Â¹ + bâ�»Â¹)â�»Â¹ less than (aâ�»Â¹bâ�»Â¹)â�»Â¹?

(1) a = 2b

(2) a + b > 1

Statement 1: a = 2b

Try 2 and 1.

(1/2 + 1)â�»Â¹ = 2/3 (1/2 * 1)â�»Â¹ = 2 The answer is yes.

Try 2/3 and 1/3. (a + b = 1)

(3/2 + 3)â�»Â¹ = 2/9 (3/2 * 3)â�»Â¹ = 2/9 The answer is no.

So we can get two different answers when using Statement 1.

Insufficient.

Statement 2: a + b > 1

We can manipulate the question in the following way.

Is (aâ�»Â¹ + bâ�»Â¹)â�»Â¹ < (aâ�»Â¹bâ�»Â¹)â�»Â¹?

Is (1/a + 1/b)â�»Â¹ < (1/ab)â�»Â¹?

Is ((a + b)/(ab))â�»Â¹ < (1/ab)â�»Â¹?

Is ab/(a + b) < ab?

Is 1 < a + b?

From Statement 2 we know that the answer is yes.

Sufficient.

The correct answer is B

Marty Murray

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- sanju09
- GMAT Instructor
**Posts:**3650**Joined:**21 Jan 2009**Location:**India**Thanked**: 267 times**Followed by:**81 members**GMAT Score:**760

Rephrasing: If a and b are positive, is (ab)/ (a + b) < ab? Since, ab > 0, a + b > 0 question reduces to: Is 1/ (a + b) < 1 orssyohee wrote: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

Statement(1) ALONE is sufficient, but statement (2) alone is not sufficient.

Statement(2) ALONE is sufficient, but statement (1) alone is not sufficient.

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

EACH statement ALONE is sufficient.

Statements (1) and (2) TOGETHER are NOT sufficient.

B

Is a + b > 1?

(1) a = 2b

When b = 1, a = 2, is 3 > 1? YES

When b = 0.1, a = 0.2, is 0.3 > 1? NO

Insufficient

(2) a + b > 1

This is what the question asking, hence [spoiler]

**YES**

Sufficient (B)[/spoiler]

Sufficient (B)

The mind is everything. What you think you become. -Lord Buddha

Sanjeev K Saxena

Quantitative Instructor

The Princeton Review - Manya Abroad

Lucknow-226001

www.manyagroup.com

Sanjeev K Saxena

Quantitative Instructor

The Princeton Review - Manya Abroad

Lucknow-226001

www.manyagroup.com