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What is the value of the 2-digit positive integer n if its

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by Max@Math Revolution » Fri Sep 07, 2018 12:11 am

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[Math Revolution GMAT math practice question]

What is the value of the 2-digit positive integer n if its tens digit is four times its units digit?

1) n is an even number
2) The units digit of n is greater than 1
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Fri Sep 07, 2018 6:58 am
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

What is the value of the 2-digit positive integer n if its tens digit is four times its units digit?

1) n is an even number
2) The units digit of n is greater than 1
Target question: What is the value of the 2-digit positive integer n

Given: Its tens digit is four times its units digit
This is VERY LIMITING information.
In fact, this tells us that EITHER n = 41 OR n = 82
There are no other possible values of n.

Statement 1: n is an even number
We already know that n is either 41 or 82
So, statement 1 tells us that n must equal 82
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The units digit of n is greater than 1
We already know that n is either 41 or 82
So, statement 2 tells us that n must equal 82
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: D

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Max@Math Revolution » Sun Sep 09, 2018 5:19 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.

The only positive two-digit integers n satisfying the original condition are 82 and 41.

Condition 1) is sufficient since 82 is the only one of these integers that is even.
Condition 2) is also sufficient, since 82 the only one of these integers with a units digit that is greater than 1.
Therefore, D is the answer.

Answer: D
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by fskilnik@GMATH » Mon Sep 17, 2018 8:56 am
Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

What is the value of the 2-digit positive integer n if its tens digit is four times its units digit?

1) n is an even number
2) The units digit of n is greater than 1
\[? = N = \left\langle {{\text{AB}}} \right\rangle \,\,\,,\,\,\,\,A,B\,\,{\text{digits}}\,\,,\,\,\,0 < A = 4B\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\{ \begin{gathered}
\,\left( {A,B} \right) = \left( {4,1} \right)\,\, \hfill \\
\,\,{\text{OR}} \hfill \\
\left( {A,B} \right) = \left( {8,2} \right) \hfill \\
\end{gathered} \right.\,\,\,\,\,\,\left( * \right)\]
\[\left( 1 \right)\,\,B \in \left\{ {0,2,4,6,8} \right\}\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,N = 82\,\,\,\,\,\, \Rightarrow {\text{SUFF}}.\]
\[\left( 2 \right)\,\,B > 1\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,N = 82\,\,\,\,\,\, \Rightarrow {\text{SUFF}}.\]

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
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