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An institute charges $n/2 for one time registration

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erica29
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An institute charges $n/2 for one time registration [#permalink] New post   03 May 2020, 13:25
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83% (00:57) correct 16% (03:32) wrong based on 6 sessions

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An institute charges $n/2 for one time registration and $3n/2 per session for first "n" sessions after which each session is charged $n only. If a student paid $60 for (n+4) sessions he attended, including the registration fee, what is the value of n?

A. 4
B. 5
C. 6
D. 7
E. 8
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B
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vndnjn
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Re: Equations [#permalink] New post   03 May 2020, 19:03
registration fee + fee for first n sessions + 4*n(for each session) = 60
n/2+3n/2+4n=60;
6n=60;
n=10

I guess ans should be 10
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erica29
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Re: Equations [#permalink] New post   03 May 2020, 20:55
Hi thanks for taking the time to answer. But N =10 is not one of the options.

Regards

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rishabhrbs96
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Re: Equations [#permalink] New post   03 May 2020, 21:18
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vndnjn wrote:
registration fee + fee for first n sessions + 4*n(for each session) = 60
n/2+3n/2+4n=60;
6n=60;
n=10

I guess ans should be 10


fee for first n sessions is 3n/2 "per session", so

n/2 + (n * 3n/2) + 4n = 60
=> 3(n^2)/2 + 9n/2 - 60 = 0
=> 3(n^2) + 9n - 120 = 0
=> (n^2) + 3n - 40 = 0
=> (n - 5)*(n + 8) = 0
=> n = 5 or n = -8

So, answer is B
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vndnjn
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Re: Equations [#permalink] New post   04 May 2020, 04:32
rishabhrbs96 wrote:
vndnjn wrote:
registration fee + fee for first n sessions + 4*n(for each session) = 60
n/2+3n/2+4n=60;
6n=60;
n=10

I guess ans should be 10


fee for first n sessions is 3n/2 "per session", so

n/2 + (n * 3n/2) + 4n = 60
=> 3(n^2)/2 + 9n/2 - 60 = 0
=> 3(n^2) + 9n - 120 = 0
=> (n^2) + 3n - 40 = 0
=> (n - 5)*(n + 8) = 0
=> n = 5 or n = -8

So, answer is B




Thanks for the correction :)
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erica29
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Re: An institute charges $n/2 for one time registration [#permalink] New post   04 May 2020, 15:55
yes absolutely correct!

Thank you!!
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gmatclubot
Re: An institute charges $n/2 for one time registration [#permalink]
04 May 2020, 15:55
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