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
For integers a, b, c, a/(b - c)=1 what is the value of (b-c)
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Given: a/(b - c) = 1BTGmoderatorDC 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
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
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\[\left\{ \begin{gathered}BTGmoderatorDC wrote:For integers a, b, c, a/(b - c)=1 what is the value of (b-c)/b ?
(1) a/b=3/5
(2) a and b have no common factors greater than 1
Source: Veritas Prep
\,a,b,c\,\,{\text{ints}}\,\, \hfill \\
\,\frac{a}{{b - c}} = 1 \hfill \\
\end{gathered} \right.\,\,\,\,\,\, \Rightarrow \,\,\,\,\,a = b - c\,\,\,\,\,\left( * \right)\]
\[? = \frac{{b - c}}{b}\]
\[\left( 1 \right)\,\,\frac{a}{b} = \frac{3}{5}\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\left( {? = } \right)\,\,\frac{{b - c}}{b} = \frac{3}{5}\,\,\,\]
\[\left( 2 \right)\,\,\,GCF\left( {a,b} \right) = 1\,\,\,\left\{ \begin{gathered}
\,{\text{Take}}\,\,\left( {a,b,c} \right) = \left( {1,2,1} \right)\,\,\,\,\,\,\, \Rightarrow \,\,\,\,{\text{?}}\,\, = \frac{1}{2} \hfill \\
\,{\text{Take}}\,\,\left( {a,b,c} \right) = \left( {1,3,2} \right)\,\,\,\,\,\,\, \Rightarrow \,\,\,\,{\text{?}}\,\, = \frac{1}{3}\,\, \hfill \\
\end{gathered} \right.\]
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)
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