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If n is contained in the set A, n+5 is contained in set A. I

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by Max@Math Revolution » Fri Nov 09, 2018 12:13 am

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[Math Revolution GMAT math practice question]

If n is contained in the set A, n+5 is contained in set A. Is 50 contained in set A?

1) 30 is contained in the set A.
2) 100 is contained in the set S
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Source: — Data Sufficiency |
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by fskilnik@GMATH » Fri Nov 09, 2018 10:45 am

If n belongs to the set A, then n+5 belongs to the set A. Does 50 belong to the set A?

1) 30 belongs to the set A.
2) 100 belongs to the set A.

Another option: If n is a member of the set A, then n+5 is a member of the set A. Is 50 a member of the set A?
Etc.

\[n \in A\,\,\,\, \Rightarrow \,\,\,\,n + 5\,\, \in \,\,A\,\,\,\,\left( * \right)\]
\[50\,\,\,\mathop \in \limits^? \,\,\,A\]
\[\left( 1 \right)\,\,\,30 \in A\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,35 \in A\,\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,40 \in A\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,45 \in A\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \]
\[\left( 2 \right)\,\,100 \in A\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,105 \in A\,\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,110 \in A\,\,\,\, \ldots \,\,\,\,\,\,\,\left\{ \begin{gathered}
\,{\text{Take}}\,\,A = \left\{ {45,50,55,60, \ldots } \right\}\,\,\,\, \Rightarrow \,\,\,\left\langle {{\text{YES}}} \right\rangle \,\, \hfill \\
\,{\text{Take}}\,\,A = \left\{ {100,105,110, \ldots } \right\}\,\,\,\, \Rightarrow \,\,\,\left\langle {{\text{NO}}} \right\rangle \,\, \hfill \\
\end{gathered} \right.\,\,\]

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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by Max@Math Revolution » Sun Nov 11, 2018 9:45 pm
=>

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

Condition 1)
Since 30 is in the set A, 35, 40, 45, 50 are in the set A.
Condition 1) is sufficient.

Condition 2)
A = { 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, ... }
The set A has 40.
But the set A = { 100, 105, 110, ... } does not have 40.
Condition 2) is not sufficient.

Therefore, A is the answer.
Answer: A
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