[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
a and b are positive numbers. What is the value of (a-b)/(a+
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- Max@Math Revolution
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Target question: What is the value of (a - b)/(a + b)?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
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
- Max@Math Revolution
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=>
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
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
Math Revolution
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Score an excellent Q49-51 just like 70% of our students.
[Free] Full on-demand course (7 days) - 100 hours of video lessons, 490 lesson topics, and 2,000 questions.
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