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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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Math Expert
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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06 Oct 2017, 05:30
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Difficulty:

55% (hard)

Question Stats:

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

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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
[Reveal] Spoiler: OA

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

Director
Joined: 25 Feb 2013
Posts: 542

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

Location: India
Schools: Mannheim"19 (S)
GPA: 3.82
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, 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

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

Manager
Joined: 12 Feb 2017
Posts: 71

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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.

Kudos [?]: 21 [0], given: 40

Retired Moderator
Joined: 05 Jul 2006
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Kudos [?]: 442 [0], given: 49

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

Kudos [?]: 442 [0], given: 49

Manager
Joined: 06 Aug 2017
Posts: 72

Kudos [?]: 13 [0], given: 27

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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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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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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