120 tickets are to be evenly distributed to n people. If n

Max@Math Revolution wrote:[Math Revolution GMAT math practice question]

120 tickets are to be evenly distributed to n people. If n is greater than 1 and the number of tickets given to each person is greater than 1, what is the greatest possible value of n?

A. 9
B. 10
C. 12
D. 14
E. 15

$${\rm{Each}}\,\,{\rm{person}}:\,\,{{120} \over n}\,\,\left( {{\mathop{\rm int}} } \right)\,\,\,{\rm{tickets}}$$
$$2 \le n \le 119\,\,{\mathop{\rm int}} $$
$$? = {n_{\max }}\,\,\,\,\, \Leftrightarrow \,\,\,\,\,{\rm{max}}\,\,{\rm{divisor}}\,\,{\rm{of}}\,\,120\,\,{\rm{less}}\,\,{\rm{that}}\,\,120$$

$${\rm{pairs}}\,\,{\rm{of}}\,\,{\rm{positive}}\,\,{\rm{divisors}}\,\,{\rm{of}}\,\,120:\left( {1,120} \right),\left( {2,60} \right), \ldots $$
$$\left( {2,60} \right)\,\,\,\left\{ \matrix{
\,2:{\rm{second}}\,\,{\rm{smaller}}\,\,{\rm{positive}}\,\,{\rm{divisor}} \hfill \cr
\,? = 60:{\rm{second}}\,\,{\rm{greater}}\,\,{\rm{positive}}\,\,{\rm{divisor}} \hfill \cr} \right.$$

Conclusion: the correct answer (60) is not among the alternative choices.


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

Regards,
Fabio.

=>

120 = 2^3*3^1*5^1 or 120 = 8*15.
Thus 15 is the greatest factor among choices.

Therefore, the answer is E.
Answer: E

Max@Math Revolution wrote:=>

120 = 23*31*51 or 120 = 8*15.
Thus 15 is the greatest factor among choices.

Therefore, the answer is E.
Answer: E

The calculation shown in red is wrong and our focus need NOT be taken among the alternative choices only.

Regards,
Fabio.

fskilnik@GMATH wrote:

Max@Math Revolution wrote:=>

120 = 23*31*51 or 120 = 8*15.
Thus 15 is the greatest factor among choices.

Therefore, the answer is E.
Answer: E

The calculation shown in red is wrong and our focus need NOT be taken among the alternative choices only.

Regards,
Fabio.

Hello, Fabio

We edited thw solutions.

Thanks.