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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## If n is contained in the set A, n+5 is contained in set A. I tagged by: Max@Math Revolution ##### This topic has 2 expert replies and 0 member replies ### GMAT/MBA Expert ## If n is contained in the set A, n+5 is contained in set A. I ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult [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 _________________ Math Revolution Finish GMAT Quant Section with 10 minutes to spare. The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. Only$149 for 3 month Online Course
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### GMAT/MBA Expert

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Quote:
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.

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### GMAT/MBA Expert

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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.

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