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venn diagram question

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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venn diagram question

by Gurpinder » Mon Jul 26, 2010 12:06 pm
In a class of 120 students numbered 1 to 120, all even numbered students opt for Physics, whose numbers are divisible by 5 opt for Chemistry and those whose numbers are divisible by 7 opt for Math. How many opt for none of the three subjects?


... so 60 students in physics
24 students in chemistry
17 students in math.....

this is all i am able to do? what am i suppose to do next? to me I think since the double-category group is missing, i am unable to find the "neither".
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by nvb8181 » Mon Jul 26, 2010 6:30 pm
Ans is 41.
To explain this.
1) No of Physics (P) studs -- 60 (all even nos starting from 2 to 120)
2) No of Chemistry (C) studs -- 24 (5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 1205, 110, 115, 120).
3) No of Maths (M) studs -- 17 (7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98, 105, 112, 119)
4) P U C U M --- 1 (only 70)
5) P U C --- 11 ( 10, 20, 30, 40, 50, 60, 80, 90, 100, 110, 120)
6) C U M --- 2 (35, 105)
7) P U M --- 7 (14, 28, 42, 56, 84, 98, 112)

So considering all the above 7 points
8)no of students opted only for Physics --> 1- (4+5+7) = 60 - (1+11+7) = 41
9)no of students opted only for Chemistry --> 2-(4+5+6) = 24 - (1+11+2) = 10
10)no of students opted only for Maths --> 3-(4+6+7) = 17 - (1+2+7) = 7

11)Total no of students opted for atleast one of the 3 subjects --> (8+9+10+4+5+6+7) --> 41+10+1+11+2+7 = 79

So No of students opted of none of the subject will be --> 120 - (11) = 120 - 79 = 41
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by outreach » Mon Jul 26, 2010 10:11 pm
students who took at least one subjects(A B C) = A + B + C - present in 2 sets(A- B + B -C + C -A) + present in all sets(A - B - C) - (1)
A - physics = 120/2=60
B - chemistry = 120/5 =24
C - math = 120/7=17

A - B = 120/(2*5)=12
B - C = 120/(5*7)= 3
C - A = 120/(2*7) =8

A - B -C = 120/(2*5*7)=1

students who took at least one subjects(A B C) = 60 + 24 + 17 - (12 + 8 + 3) + 1 = 79
none of the three subjects= TOTAL - students who took at least one subjects(A B C)=1
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