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

Question

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

Are You Up For the Challenge: 700 Level Questions

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

Are You Up For the Challenge: 700 Level Questions

LevanKhukhunashvili · Answer

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

Ansh777 · Answer

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
Answer = B

ScottTargetTestPrep · Answer

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

Answer: B

ottomankhan · Answer

Let the total number of badges =B and total students =S

Badges the student got=B/6

Badges other students got=B*5/6=5B/6

the number of other students= S-1

now
B/6= 5B*5/6(s-1)
S= 26

Posted from my mobile device

sharma789 · Answer

hi
i have one question that why we are subtracting 1 from number of students. can anyone answer my query

LuffyTaro · Answer

Hi, we subtract one because it says that one student got one sixth of the average number of badges all the other students got, so we are finding the average number of badges for all the students minus that one particular student which means the count of students in this case becomes total students - 1.

Posted from my mobile device

bumpbot · Answer

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

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