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29 Jan 2019, 03:16
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MathRevolution
#1
n can be 0,4,8,12... and always the sum of \(4^n+n^2+1\) would be odd which is not divisible by 2 ; sufficient
#2
n can be 0,6,12,18... and always the sum of \(4^n+n^2+1\) would be odd which is not divisible by 2 ; sufficient
IMO D
29 Jan 2019, 06:02
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MathRevolution
\(?\,\, = \,\,0\# 1\,\,\,\,\,\,\left( {\# \in \left\{ { + , - , \times , \div } \right\}} \right)\)
\(\left( 1 \right)\,\,2\# 1 = 2\,\,\,\, \Rightarrow \left\{ \matrix{\\
\,\,\# = \times \,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = 0 \hfill \cr \\
\,\,{\rm{OR}} \hfill \cr \\
\,\,\# = \div \,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = 0 \hfill \cr} \right.\,\,\,\, \Rightarrow \,\,\,\,\,\,{\rm{SUFF}}{\rm{.}}\)
\(\left( 2 \right)\,\,\,\,4\# 2 = 2\,\,\,\, \Rightarrow \left\{ \matrix{\\
\,\,\# = - \,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = - 1 \hfill \cr \\
\,\,{\rm{OR}} \hfill \cr \\
\,\,\# = \div \,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = 0 \hfill \cr} \right.\,\,\,\, \Rightarrow \,\,\,\,\,\,{\rm{INSUFF}}{\rm{.}}\)
The correct answer is therefore (A).
We follow the notations and rationale taught in the GMATH method.
Regards,
Fabio.
Updated on: 26 May 2021, 02:50
Originally posted by MathRevolution on 30 Jan 2019, 02:20.
Last edited by MathRevolution on 26 May 2021, 02:50, edited 1 time in total.
Last edited by MathRevolution on 26 May 2021, 02:50, edited 1 time in total.
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MathRevolution
=>
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.
Since \(4^n\) is a multiple of \(2\), we only need to look at \(n^2+1\).
If \(n\) is an odd number, \(4^n+n^2+1\) is divisible by \(2\).
If \(n\) is an even number, \(4^n+n^2+1\) is not divisible by \(2\).
The question asks if \(n\) is an odd number.
Thus, each of conditions is sufficient.
Therefore, D is the answer.
Answer: D
