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For integers a, b, and c, a/(b-c) = 1. What is the value of (b-c)/b?
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Updated on: 30 Aug 2019, 04:17
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Bunuel wrote:
For integers a, b, and c, a/(b-c) = 1. What is the value of (b-c)/b?
(1) a/b = 3/5
(2) a and b have no common factors greater than 1
Given \(\frac{a}{(b-c)}=1 => b-c=a\)
to find \(\frac{(b-c)}{b}=\frac{a}{b}\)
Statement 1: Directly provides the answer. Hence Sufficient
Statement 2: when you divide \(a\) by \(b\) common factors get cancelled out but the non common factors / primes remain whose information is not provided. So \(\frac{a}{b}\) cannot be calculated. Insufficient
Option A
Originally posted by niks18 on 06 Oct 2017, 05:43.
Last edited by niks18 on 30 Aug 2019, 04:17, edited 1 time in total.
Re: For integers a, b, and c, a/(b-c) = 1. What is the value of (b-c)/b?
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06 Oct 2017, 15:20
Bunuel wrote:
For integers a, b, and c, a/(b-c) = 1. What is the value of (b-c)/b?
(1) a/b = 3/5
(2) a and b have no common factors greater than 1
The answer should be A as follows.
Given \(\frac{a}{(b-c)}=1\)
1. Condition A gives \frac{a}{b}=\(3/5\) == \(a=\frac{3}{5}*b\) Putting this value of "a" in the given condition we get \(\frac{a}{(b-c)}=1\)==>\(((3/5)*b)/(b-c)=1\)==>\(\frac{b}{(b-c)}\)=\(1*\frac{5}{3}\)==>\(\frac{b}{(b-c)}\)=\(\frac{5}{3}\)==>\(\frac{(b-c)}{b}\)=\(\frac{3}{5}\) SUFFICIENT
2. a and b have no common factors greater than 1 ==> This neither provide any clue about the value of a and b nor provide any relation between a and b that can be substituted in the given equation to solve. INSUFFICIENT
Re: For integers a, b, and c, a/(b-c) = 1. What is the value of (b-c)/b?
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29 Oct 2018, 06:25
Top Contributor
Expert Reply
Bunuel wrote:
For integers a, b, and c, a/(b-c) = 1. What is the value of (b-c)/b?
(1) a/b = 3/5
(2) a and b have no common factors greater than 1
Given: a/(b - c) = 1
Target question:What is the value of (b-c)/b ? This is a good candidate for rephrasing the target question. Aside: The video below has tips on rephrasing the target question If a/(b - c) = 1, then we know that a = b - c The target question asks "What is the value of (b-c)/b ?" Since a = b - c, we can replace b - c with a to get: REPHRASED target question:What is the value of a/b ?
Statement 1: a/b = 3/5 Perfect! The answer to the REPHRASED target question is a/b = 3/5 Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT
Statement 2: a and b have no common factors greater than 1 There are several values of a and b that satisfy statement 2. Here are two: Case a: a = 1 and b = 2. In this case, the answer to the REPHRASED target question is a/b = 1/2 Case b: a = 2 and b = 3. In this case, the answer to the REPHRASED target question is a/b = 2/3 Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
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Re: For integers a, b, and c, a/(b-c) = 1. What is the value of (b-c)/b?
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03 Nov 2019, 09:49
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