[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
120 tickets are to be evenly distributed to n people. If n
This topic has expert replies
- Max@Math Revolution
- Elite Legendary Member
- Posts: 3991
- Joined: Fri Jul 24, 2015 2:28 am
- Location: Las Vegas, USA
- Thanked: 19 times
- Followed by:37 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
Last edited by Max@Math Revolution on Mon Dec 24, 2018 6:35 am, edited 1 time in total.
Math Revolution
The World's Most "Complete" GMAT Math Course!
Score an excellent Q49-51 just like 70% of our students.
[Free] Full on-demand course (7 days) - 100 hours of video lessons, 490 lesson topics, and 2,000 questions.
[Course] Starting $79 for on-demand and $60 for tutoring per hour and $390 only for Live Online.
Email to : [email protected]
- fskilnik@GMATH
- GMAT Instructor
- Posts: 1449
- Joined: Sat Oct 09, 2010 2:16 pm
- Thanked: 59 times
- Followed by:33 members
$${\rm{Each}}\,\,{\rm{person}}:\,\,{{120} \over n}\,\,\left( {{\mathop{\rm int}} } \right)\,\,\,{\rm{tickets}}$$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
$$2 \le n \le 119\,\,{\mathop{\rm int}} $$
$$? = {n_{\max }}\,\,\,\,\, \Leftrightarrow \,\,\,\,\,{\rm{max}}\,\,{\rm{divisor}}\,\,{\rm{of}}\,\,120\,\,{\rm{less}}\,\,{\rm{that}}\,\,120$$
$${\rm{pairs}}\,\,{\rm{of}}\,\,{\rm{positive}}\,\,{\rm{divisors}}\,\,{\rm{of}}\,\,120:\left( {1,120} \right),\left( {2,60} \right), \ldots $$
$$\left( {2,60} \right)\,\,\,\left\{ \matrix{
\,2:{\rm{second}}\,\,{\rm{smaller}}\,\,{\rm{positive}}\,\,{\rm{divisor}} \hfill \cr
\,? = 60:{\rm{second}}\,\,{\rm{greater}}\,\,{\rm{positive}}\,\,{\rm{divisor}} \hfill \cr} \right.$$
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
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
- Max@Math Revolution
- 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 = 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
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
Math Revolution
The World's Most "Complete" GMAT Math Course!
Score an excellent Q49-51 just like 70% of our students.
[Free] Full on-demand course (7 days) - 100 hours of video lessons, 490 lesson topics, and 2,000 questions.
[Course] Starting $79 for on-demand and $60 for tutoring per hour and $390 only for Live Online.
Email to : [email protected]
- fskilnik@GMATH
- GMAT Instructor
- Posts: 1449
- Joined: Sat Oct 09, 2010 2:16 pm
- Thanked: 59 times
- Followed by:33 members
The calculation shown in red is wrong and our focus need NOT be taken among the alternative choices only.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
Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br
- Max@Math Revolution
- Elite Legendary Member
- Posts: 3991
- Joined: Fri Jul 24, 2015 2:28 am
- Location: Las Vegas, USA
- Thanked: 19 times
- Followed by:37 members
Hello, Fabiofskilnik@GMATH wrote:The calculation shown in red is wrong and our focus need NOT be taken among the alternative choices only.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
Regards,
Fabio.
We edited thw solutions.
Thanks.
Math Revolution
The World's Most "Complete" GMAT Math Course!
Score an excellent Q49-51 just like 70% of our students.
[Free] Full on-demand course (7 days) - 100 hours of video lessons, 490 lesson topics, and 2,000 questions.
[Course] Starting $79 for on-demand and $60 for tutoring per hour and $390 only for Live Online.
Email to : [email protected]