The question doesn't tell the amount of the women so I think the "120 men" mean that there are "120 people"(men+women) in the class.
That mean 46 people which are not "above group" consist of 2/5 men(without beards) and 1/3 women(without long hair).
You can get this equation:
46= 2/5men + 1/3women
74= 3/5men + 2/3women
120= men + women
You can change the first equation into this
46= 2/5men + 1/3women
1/3women= 46- 2/5 men
women= 138- 6/5 men
Add the first equation into the second
74= 3/5men + 2/3women
74= 3/5men + 2/3(138- 6/5 men)
74= 3/5men + 92- 4/5men
74= -1/5 men + 92
1/5 men= 92-74
men= 18 *5= 90
Using the 3rd equation
120= men + women
women= 120-90= 30
The answer would be: 90 men, 30 women
