If a and b are positive...

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If a and b are positive...

by ssyohee » Mon Feb 01, 2016 8:35 am
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

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by Marty Murray » Mon Feb 01, 2016 11:18 am
ssyohee 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
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.

Statement 1: a = 2b

Try 2 and 1.

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

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

(3/2 + 3)�¹ = 2/9 (3/2 * 3)�¹ = 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 (a�¹ + b�¹)�¹ < (a�¹b�¹)�¹?

Is (1/a + 1/b)�¹ < (1/ab)�¹?

Is ((a + b)/(ab))�¹ < (1/ab)�¹?

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
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by sanju09 » Fri Feb 05, 2016 1:39 am
ssyohee 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
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 or

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]
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