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

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Intern
Joined: 09 Apr 2017
Posts: 25
Location: Nepal
Concentration: Finance, Entrepreneurship
WE: Information Technology (Computer Software)
A certain number of badges were distributed among a class of students.  [#permalink]

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04 Sep 2018, 01:25
3
00:00

Difficulty:

85% (hard)

Question Stats:

43% (02:27) correct 57% (01:39) wrong based on 32 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. 30
b. 26
c. 11
d. 31
e. 50
Intern
Joined: 30 May 2017
Posts: 16
Re: A certain number of badges were distributed among a class of students.  [#permalink]

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04 Sep 2018, 01:56
B - Total number of Badges
N - Number of students

Translating the text into an equation, we get:

1/6 B =5*(5/6B)/(N-1)

Target Test Prep Representative
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A certain number of badges were distributed among a class of students.  [#permalink]

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07 Sep 2018, 16:01
pratik2018 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. 30
b. 26
c. 11
d. 31
e. 50

We can let the total number of badges = n and the total number of students = q. Since one student gets 1/6 of the badges, the remaining students get 5n/6 of the badges. Thus the average number of badges the others got = (5n/6)/(q - 1), and we have:

(1/6)(n) = 5((5n/6)/(q - 1))

(1/6)n(q - 1) = 5(5n/6)

(q - 1)/6 = 25/6

q - 1= 25

q = 26

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A certain number of badges were distributed among a class of students.   [#permalink] 07 Sep 2018, 16:01
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