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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- MartyMurray
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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 (a�¹ + b�¹)�¹ less than (a�¹b�¹)�¹?
(1) a = 2b
(2) a + b > 1
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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- sanju09
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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]
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Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com