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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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Joined: 02 Sep 2009
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Kudos [?]: 132595 [0], given: 12326

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

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New post 06 Oct 2017, 05:30
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A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

74% (00:46) correct 26% (00:44) wrong based on 39 sessions

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Kudos [?]: 132595 [0], given: 12326

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Kudos [?]: 246 [0], given: 33

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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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New post 06 Oct 2017, 06:43
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 \(\frac{(b-c)}{a}=\frac{a}{b}\)

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

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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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New post 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.

Answer is Option A.

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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New post 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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GMAT 1: 610 Q48 V24
For integers a, b, and c, a/(b-c) = 1. What is the value of (b-c)/b? [#permalink]

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New post 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

Hence answer is A
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For integers a, b, and c, a/(b-c) = 1. What is the value of (b-c)/b?   [#permalink] 06 Oct 2017, 16:20
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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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