Tough 3 Sets Prob

[cramya]

In a hostel of 100 students, 42 are science graduates, 34 are law graduates and 58 are commerce graduates. 8 students are science and law graduates, 13 students are law and commerce graduates, 18 students are commerce and science graduates. Every student takes atleast one course.How many students are only science graudates?


A)23
B)22
C)21
D)34
E)19


OA C

[Reader]

First step is to get number of student that take all three class. which is
100-(42+34+58-8-13-18) =5

Now out of 8 students who are science and law graduates and 18 students who are are commerce and science graduates there is 5 of them who took all three so they are counted twice.

so 42 - (18 + 8 - 5) =21

[logitech]

100 = S+ C + L - ( SC + SL + LC ) + SLC
100 = 42+34+58 - ( 39 ) + SLC

SLC = 5

Since we want to find only Science Graduates:

= 42 + SLC - (SL+SC)
= 42 + 5 - 26
= 21

ALTERNATIVELY:

If you look at the second equation, you will realize that we can insert it into the first one

42 + SLC - (SL+SC) = is what questions asks us (LET'S CALL IT X) and
100 = S+ C + L - ( SC + SL + LC ) + SLC is the first equation

So the question actually boils down to:

100 = X + C + L - LC

100 = X + 58 + 34 - 13

X = 21

[logitech]

And this is how I remember the rules, hope this helps!