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

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by Max@Math Revolution » Wed Dec 19, 2018 11:49 pm

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[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 from choices?

A. 9
B. 10
C. 12
D. 14
E. 15
Last edited by Max@Math Revolution on Mon Dec 24, 2018 6:35 am, edited 1 time in total.
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by fskilnik@GMATH » Thu Dec 20, 2018 1:53 am
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.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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EDIT

by Max@Math Revolution » Sun Dec 23, 2018 6:07 pm
=>

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
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by fskilnik@GMATH » Sun Dec 23, 2018 6:13 pm
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.
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by Max@Math Revolution » Sun Dec 23, 2018 10:53 pm
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.
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