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31 Jan 2024, 02:30
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87% (02:03) correct
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A total of 45 male and female students took a math test. The male students have an average score of 65, and the female students have an average score of 70. If the overall average score for both male and female students is 67, how many male students participated in the test?
A. 27
B. 31
C. 33
D. 35
E. 37
A. 27
B. 31
C. 33
D. 35
E. 37
A total of \(45\) male and female students take a math test. The average score for the male students is \(65\) and the average score for the female students is \(70\). Also, the combined average score for the male and female students is \(67\). How many male students took the test?
Aryaa03
Joined: 12 Jun 2023
Last visit: 13 Jun 2025
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Location: India
Schools: ISB '27 (A) IIM Calcutta '26 (A) IIMA '26 (D)
GMAT Focus 1: 645 Q86 V81 DI78 
31 Jan 2024, 04:52
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Bunuel
A total of 45 male and female students took a math test. The male students have an average score of 65, and the female students have an average score of 70. If the overall average score for both male and female students is 67, how many male students participated in the test?
A. 27
B. 31
C. 33
D. 35
E. 37
A. 27
B. 31
C. 33
D. 35
E. 37
Sol: IMO Option-A
Say , number of males be M and number of females are F
Given, M + F= 45
Average score - Males = 65
Average score - Females = 70
Combined average = 67
Using differential technique of weighted average :
(67-65)*M + (67-70)*F = 0
2M - 3F = 0
2M = 3F
M/F = 3/2
Let common multiple for the ratio be x
==> 3x + 2x = 45 ==> 5x = 45
x =9
No. of male = 3x = 3*9= 27
31 Jan 2024, 06:49
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Option A should be correct.
This is a simple question of alligation method or we can solve it with weighted average method also.
let m+f=45 [m=number of males, f= number of females]
we know 65*m + 70*f = 67 * 45
=> 65*m + 70*f = 67 * (m+f) = 67*m + 67*f
=> 2*m = 3*f
=> m:f = 3:2
So number of male students = 45*\(\frac{3}{(3+2)}\) = 27
Hence, correct option should be A
This is a simple question of alligation method or we can solve it with weighted average method also.
let m+f=45 [m=number of males, f= number of females]
we know 65*m + 70*f = 67 * 45
=> 65*m + 70*f = 67 * (m+f) = 67*m + 67*f
=> 2*m = 3*f
=> m:f = 3:2
So number of male students = 45*\(\frac{3}{(3+2)}\) = 27
Hence, correct option should be A
