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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 ## n is a positive integer. Is n divisible by 3? tagged by: Max@Math Revolution ##### This topic has 2 expert replies and 0 member replies ### GMAT/MBA Expert ## n is a positive integer. Is n divisible by 3? ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult [Math Revolution GMAT math practice question] n is a positive integer. Is n divisible by 3? 1) 36/n is divisible by 3 2) 27/n is divisible by 3 _________________ 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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Max@Math Revolution wrote:
[Math Revolution GMAT math practice question]

n is a positive integer. Is n divisible by 3?

1) 36/n is divisible by 3
2) 27/n is divisible by 3
$$n \ge 1\,\,{\mathop{\rm int}}$$
$${n \over 3}\,\,\mathop = \limits^? \,\,{\mathop{\rm int}}$$

$$\left( 1 \right)\,\,\,\left( {{{36} \over n} = {\mathop{\rm int}} \,\,{\rm{and}}} \right)\,\,\,{{12} \over n} = {{36} \over {3n}} = {\mathop{\rm int}} \,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,{\rm{n = 1}}\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \hfill \cr \,{\rm{Take}}\,\,{\rm{n = 3}}\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \hfill \cr} \right.$$

$$\left( 2 \right)\,\,\,\left( {{{27} \over n} = {\mathop{\rm int}} \,\,{\rm{and}}} \right)\,\,\,{9 \over n} = {{27} \over {3n}} = {\mathop{\rm int}} \,\,\,\left\{ \matrix{ \,\left( {{\mathop{\rm Re}\nolimits} } \right){\rm{Take}}\,\,{\rm{n = 1}}\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{NO}}} \right\rangle \hfill \cr \,\left( {{\mathop{\rm Re}\nolimits} } \right){\rm{Take}}\,\,{\rm{n = 3}}\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\rm{YES}}} \right\rangle \hfill \cr} \right.$$

$$\Rightarrow \,\,\,\,\left( {\rm{E}} \right)$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

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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.

Since we have 1 variable (n) and 0 equations in the original condition, D is most likely to be the answer. So, we should consider each condition on its own first. It is suggested we plug in numbers when solving remainder problems.

Condition 1)
If n = 3, then 36/3 = 12 is divisible by 3, and n is divisible by 3. The answer is ‘yes’.
If n = 1, then 36/1 = 36 is divisible by 3, but n is not divisible by 3. The answer is ‘no’.
Thus, condition 1) is not sufficient, since it does not yield a unique solution.

Condition 2)
If n = 3, then 27/3 = 9 and n is divisible by 3. The answer is ‘yes’.
If n = 1, then 27/1 = 27 and n is not divisible by 3. The answer is ‘no’.
Thus, condition 2) is not sufficient, since it does not yield a unique solution.

Conditions 1) & 2)
Even if we consider both conditions together, we still have two possible values of n: n = 1 and 3.
Thus, both conditions together are not sufficient, since they do not yield a unique solution.

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.

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