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26 Nov 2019, 00:13
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B
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Difficulty:
85%
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Question Stats:
48% (02:11) correct
52%
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wrong
based on 354
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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
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
26 Nov 2019, 00:33
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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
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
Joined: 03 Nov 2019
Last visit: 06 Jun 2023
Posts: 56
Given Kudos: 129
Location: India
Schools: Booth '24 Columbia CBS '24 Darden '24 Fuqua '24 Haas '24 Harvard '24 LBS '24 Stanford '24 Kellogg '24 Wharton '24
GMAT 1: 710 Q50 V36
Schools: Booth '24 Columbia CBS '24 Darden '24 Fuqua '24 Haas '24 Harvard '24 LBS '24 Stanford '24 Kellogg '24 Wharton '24
GMAT 1: 710 Q50 V36
Posts: 56
26 Nov 2019, 07:07
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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
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
