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a and b are positive numbers. What is the value of (a-b)/(a+b)?

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Math Revolution GMAT Instructor
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a and b are positive numbers. What is the value of (a-b)/(a+b)?  [#permalink]

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New post 18 Sep 2018, 02:01
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Question Stats:

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[Math Revolution GMAT math practice question]

\(a\) and \(b\) are positive numbers. What is the value of \(\frac{(a-b)}{(a+b)}\)?

\(1) a=2b\)
\(2) \frac{(a^2-b^2)}{(a+b)^2} =\frac{1}{3}\)

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Re: a and b are positive numbers. What is the value of (a-b)/(a+b)?  [#permalink]

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New post 18 Sep 2018, 02:34
From statement 1:

a = 2b.
Then, \(\frac{(a-b)}{(a+b)}\) = b/3b = 1/3.

Sufficient.

From statement 2:

\(\frac{(a^2−b^2)}{(a+b)^2}\) = \(\frac{(a+b)(a-b)}{(a+b)(a+b)}\) = \(\frac{(a-b)}{(a+b)}\) = 1/3.

Hence both are individually sufficient.

D is the answer.
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Re: a and b are positive numbers. What is the value of (a-b)/(a+b)?  [#permalink]

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New post 18 Sep 2018, 07:23
Top Contributor
MathRevolution wrote:
[Math Revolution GMAT math practice question]

\(a\) and \(b\) are positive numbers. What is the value of \(\frac{(a-b)}{(a+b)}\)?

\(1) a=2b\)
\(2) \frac{(a^2-b^2)}{(a+b)^2} =\frac{1}{3}\)


Target question: What is the value of (a - b)/(a + b)?

Statement 1: a = 2b
Take: (a - b)/(a + b)
Replace a with 2b to get: (2b - b)/(2b + b)
Simplify: b/3b
Divide top and bottom by b to get: 1/3
So, the answer to the target question is (a - b)/(a + b) = 1/3
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: (a² - b²)/(a + b)² =1/3
Take: (a² - b²)/(a + b)² =1/3
Factor top and bottom to get: (a + b)(a - b)/(a + b)(a + b) =1/3
Divide top and bottom by (a + b) to get: (a - b)/(a + b) = 1/3
So, the answer to the target question is (a - b)/(a + b) = 1/3
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent
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Re: a and b are positive numbers. What is the value of (a-b)/(a+b)?  [#permalink]

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New post 20 Sep 2018, 01:57
=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

When a question asks for a ratio, the condition including the ratio is most likely to be sufficient. This tells us that D is most likely to be the answer to this question.

Condition 1)
\(a = 2b\) is equivalent to \(\frac{a}{b} = 2\).
So, \(\frac{(a-b)}{(a+b)} = { (\frac{a}{b}) – 1 } / { (\frac{a}{b}) + 1 } = \frac{( 2 – 1 )}{( 2 + 1 )} = \frac{1}{3}.\)
Condition 1) is sufficient.

Condition 2)
\(\frac{(a^2-b^2)}{(a+b)^2} =\frac{1}{3}\)
\(=> \frac{(a-b)(a+b)}{(a+b)^2} =\frac{1}{3}\)
\(=> \frac{(a-b)}{(a+b)} =\frac{1}{3}\)
Condition 2) is sufficient.

FYI, Tip 1) of VA method states that D is most likely to be the answer if conditions 1) and 2) provide the same information.

Therefore, D is the answer.
Answer: D
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Re: a and b are positive numbers. What is the value of (a-b)/(a+b)? &nbs [#permalink] 20 Sep 2018, 01:57
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