BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

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

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 am
Location: Las Vegas, USA
Thanked: 19 times
Followed by:37 members

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

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

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

[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.
Top
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 1449
Joined: Sat Oct 09, 2010 2:16 pm
Thanked: 59 times
Followed by:33 members

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)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
Top
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 am
Location: Las Vegas, USA
Thanked: 19 times
Followed by:37 members

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
Top
User avatar
GMAT Instructor
Posts: 1449
Joined: Sat Oct 09, 2010 2:16 pm
Thanked: 59 times
Followed by:33 members

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.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
Top
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 am
Location: Las Vegas, USA
Thanked: 19 times
Followed by:37 members

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.
Top
Post new topic Post Reply
• Page 1 of 1