the class opted for

[sanju09]

In a class of 50 students, 10 did not opt for math. 15 did not opt for science and 2 did not opt for either. How many students of the class opted for both math and science?

A. 37

B. 25

C. 23

D. 27

E. 48

OA D

[lav]

In a class of 50 students, 10 did not opt for math and 2 did not opt for either. Hence no of students opted for science = 50-10-2 = 38

In a class of 50 students, 15 did not opt for science and 2 did not opt for either. Hence no of students opted for maths= 50-15-2 = 33

Total = (sc) + (math) + (neither) - both
50=38+33+2-both
both = 73-50=23

according to me ans is C 23 ??
anyone agrees or disagrees ?

[scoobydooby]

guess you got mistaken in the formula

Total = (sc) + (math) + (neither) - both
here we do not take out "niether" once from science and once from maths. niether is subtracted just once from Total. subtracting from science and maths would mean subtracting twice extra

in effect we should have

50-2=40+35-both, which would give both as 27

found it easier by the 2 by 2 matrix

[quocbao]

50-2=40+35-both, which would give both as 27

Can you explain about 40 & 35 ?

[scoobydooby]

50 students

10 non maths=> 50-10=40 (maths,science+maths, non science. will not include "niether" as it does not include non maths)


15 non science=50-15=35 (science, maths+science, non maths. will not include "niether" as it does not include non science)



becomes easier to visualize in a matrix format

[nightriders_leo]

The correct answer is 27 according to the formula

n(AUB) = n(A)+n(B)-n(A intersection B)
n(AUB)= 10+15-2
n(AUB)=25-2
n(AUB)=23


This means 23 students are there which have either Science or maths

so if we substract 50 - 23 = 27

So 27 students are there which have both science & maths

[lav]

thanks for correcting me scooby
I guess i solved it in a hurry , hence a silly mistake

[cubicle_bound_misfit]

IMO, It is not possible to solve with this many info.
We can find how many did not opt for math ditto for science also how many did not for both, but getting the value of how many math and science is equally important.
27 gives you a union of math and science.

Mr. Ian Stuart, if you are still around please help.

Regards,
CBM