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For integers a, b, c, a/(b - c)=1 what is the value of (b-c)

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Mon Oct 29, 2018 3:54 am

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For integers a, b, 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

OA A

Source: Veritas Prep

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Source: Beat The GMAT — Data Sufficiency | Mon Oct 29, 2018 3:54 am

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon Oct 29, 2018 6:19 am

BTGmoderatorDC 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: Here's a video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100
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

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

by fskilnik@GMATH » Mon Oct 29, 2018 7:40 am

BTGmoderatorDC wrote:For integers a, b, 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
Source: Veritas Prep

\[\left\{ \begin{gathered}
\,a,b,c\,\,{\text{ints}}\,\, \hfill \\
\,\frac{a}{{b - c}} = 1 \hfill \\
\end{gathered} \right.\,\,\,\,\,\, \Rightarrow \,\,\,\,\,a = b - c\,\,\,\,\,\left( * \right)\]
\[? = \frac{{b - c}}{b}\]
\[\left( 1 \right)\,\,\frac{a}{b} = \frac{3}{5}\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\left( {? = } \right)\,\,\frac{{b - c}}{b} = \frac{3}{5}\,\,\,\]
\[\left( 2 \right)\,\,\,GCF\left( {a,b} \right) = 1\,\,\,\left\{ \begin{gathered}
\,{\text{Take}}\,\,\left( {a,b,c} \right) = \left( {1,2,1} \right)\,\,\,\,\,\,\, \Rightarrow \,\,\,\,{\text{?}}\,\, = \frac{1}{2} \hfill \\
\,{\text{Take}}\,\,\left( {a,b,c} \right) = \left( {1,3,2} \right)\,\,\,\,\,\,\, \Rightarrow \,\,\,\,{\text{?}}\,\, = \frac{1}{3}\,\, \hfill \\
\end{gathered} \right.\]
Important: to offer a viable BIFURCATION, we must also control the value of c, so that all restrictions are shown to be obeyed.

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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