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# A certain number of badges were distributed among a class of students.

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Math Expert
Joined: 02 Sep 2009
Posts: 60540
A certain number of badges were distributed among a class of students.  [#permalink]

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26 Nov 2019, 00:13
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Difficulty:

65% (hard)

Question Stats:

54% (02:25) correct 46% (01:49) wrong based on 52 sessions

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A certain number of badges were distributed among a class of students. The student who got 1/6th of the total number of badges actually got 5 times the average number of badges the others got. How many students were there in the class?

A. 11
B. 26
C. 30
D. 31
E. 50

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Posts: 495
GMAT 1: 640 Q48 V28
Re: A certain number of badges were distributed among a class of students.  [#permalink]

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26 Nov 2019, 00:33
Let the number of badges be x
number of students be y

We can arrange an equation:
student with 1/6 of badges= 5 * (the rest of the badges -->"5x/6" divided by the number of students minus 1--> "y-1")
x/6=5*(5x/6 /y-1)
After some manipulations, we get x(y-1)=25x --> y=26

IMO
Ans: B
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Joined: 03 Nov 2019
Posts: 54
Re: A certain number of badges were distributed among a class of students.  [#permalink]

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26 Nov 2019, 07:07
Let:
Total Number of badges = T
Total Number of Students= N
Now The number of badges this student got = (1/6)*Total Number of badges =T/6
Average number of badges the other students got (excluding the badges of this student from the total) = (T-T/6)/(N-1)
Therefore
T/6 = 5*(T-T/6)/(N-1)
Simplifying
(N-1)=25
Or N=26
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Re: A certain number of badges were distributed among a class of students.  [#permalink]

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02 Dec 2019, 19:15
Bunuel wrote:
A certain number of badges were distributed among a class of students. The student who got 1/6th of the total number of badges actually got 5 times the average number of badges the others got. How many students were there in the class?

A. 11
B. 26
C. 30
D. 31
E. 50

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We can let N = the number of students and T = the total number of badges. We see that T/6 is the number of badges that the student got, and so (T - T/6) is the number of badges that the others got. We can create the equation:

T/6 = 5(T - T/6)/(N - 1)

Multiplying both sides of the equation by 6(N - 1), we obtain:

(N - 1)T = 30(T - T/6)

NT - T = 30T - 5T

NT = 26T

N = 26

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Re: A certain number of badges were distributed among a class of students.   [#permalink] 02 Dec 2019, 19:15
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