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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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For integers a, b, and c, a/(b-c) = 1. What is the value of (b-c)/b?  [#permalink]

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06 Oct 2017, 05:30
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Project DS Butler: Day 28: Data Sufficiency (DS56)

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

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For integers a, b, and c, a/(b-c) = 1. What is the value of (b-c)/b?  [#permalink]

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Updated on: 30 Aug 2019, 05:17
2
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, 06:43.
Last edited by niks18 on 30 Aug 2019, 05:17, edited 1 time in total.
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Re: For integers a, b, and c, a/(b-c) = 1. What is the value of (b-c)/b?  [#permalink]

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06 Oct 2017, 07:07
a,b and c are integers
a/(b-c) = 1
means a= (b-c)
(b-c)/b = ?

stmt 1
a/b = 3/5
substitute a= (b-c)
(b-c)/b = 3/5
Hence Sufficient.

stmt 2
a and b have no common factors greater than 1
means a and b are prime, that does not give us any idea about a/b ratio.
Hence Insufficient.

Kudos if it helps.
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Re: For integers a, b, and c, a/(b-c) = 1. What is the value of (b-c)/b?  [#permalink]

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06 Oct 2017, 08:41
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

A = B-C

What is (b-c)/b , i.e. what is a/b??

from 1

suff

from 2

a, b are co prime ...no mention of values or ratio ( depends on the unknown prime factors of each) .. insuff

A
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Re: For integers a, b, and c, a/(b-c) = 1. What is the value of (b-c)/b?  [#permalink]

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06 Oct 2017, 16:20
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

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Re: For integers a, b, and c, a/(b-c) = 1. What is the value of (b-c)/b?  [#permalink]

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29 Oct 2018, 07:25
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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: 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

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Re: For integers a, b, and c, a/(b-c) = 1. What is the value of (b-c)/b?   [#permalink] 29 Oct 2018, 07:25
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