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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
Joined: 16 Aug 2015
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a and b are positive numbers. What is the value of (a-b)/(a+b)?  [#permalink]

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18 Sep 2018, 01:01
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15% (low)

Question Stats:

78% (00:40) correct 22% (01:06) wrong based on 55 sessions

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[Math Revolution GMAT math practice question]

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

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

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $149 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Director Joined: 18 Jul 2018 Posts: 574 Location: India Concentration: Finance, Marketing WE: Engineering (Energy and Utilities) Re: a and b are positive numbers. What is the value of (a-b)/(a+b)? [#permalink] Show Tags 18 Sep 2018, 01:34 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. _________________ If you are not badly hurt, you don't learn. If you don't learn, you don't grow. If you don't grow, you don't live. If you don't live, you don't know your worth. If you don't know your worth, then what's the point? CEO Joined: 11 Sep 2015 Posts: 3341 Location: Canada Re: a and b are positive numbers. What is the value of (a-b)/(a+b)? [#permalink] Show Tags 18 Sep 2018, 06:23 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 _________________ Test confidently with gmatprepnow.com Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6815 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: a and b are positive numbers. What is the value of (a-b)/(a+b)? [#permalink] Show Tags 20 Sep 2018, 00:57 => 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$149 for 3 month Online Course"
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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, 00:57
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