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

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by Max@Math Revolution » Tue Sep 18, 2018 12:56 am

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[Math Revolution GMAT math practice question]

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

1) a=2b
2) (a^2-b^2) / (a+b)^2 =1/3
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Tue Sep 18, 2018 6:20 am
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

If a and b are positive numbers, what is the value of (a - b)/(a + b)?

1) a = 2b
2) (a² - b²)/(a + b)² =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
Brent Hanneson - Creator of GMATPrepNow.com
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by Max@Math Revolution » Thu Sep 20, 2018 12:50 am
=>

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 a/b = 2.
So, (a-b)/(a+b) = { (a/b) - 1 } / { (a/b) + 1 } = ( 2 - 1 ) / ( 2 + 1 ) = 1/3.
Condition 1) is sufficient.

Condition 2)
(a^2-b^2) / (a+b)^2 =1/3
=> (a-b)(a+b)/(a+b)^2 =1/3
=> (a-b)/(a+b) =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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