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

Question

(1) a/b = 3/5

(2) a and b have no common factors greater than 1

niks18 · Accepted Answer

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

pushkarajnjadhav · Answer

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.

Answer is Option A.

Kudos if it helps.

yezz · Answer

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

GMATisLovE · Answer

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

Hence answer is A

BrentGMATPrepNow · Answer

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

RELATED VIDEO FROM OUR COURSE
 https://www.youtube.com/watch?v=MyG1K3ee69w

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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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GMAT Data Sufficiency (DS) Questions

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

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