Set theory in CAT CMAT and other exams
Shortcuts and how to prepare video..

Brilliant question… PnC and Set theory combo..

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?

A. 19
B. 41
C. 21
D. 57
E. 26

Long cut solution:
We need to find out the number of students who took at least one of the three subjects and subtract that number from the overall 120 to get the number of students who did not opt for any of the three subjects.

Number of students who took at least one of the three subjects can be found by finding out A U B U C, where A is the set of those who took Physics, B the set of those who took Chemistry and C the set of those who opted for Math.

Now, AUBUC = A + B + C – (A n B + B n C + C n A) + (A n B n C)
A is the set of those who opted for Physics = 120/2 = 60 students
B is the set of those who opted for Chemistry = 120/5 = 24
C is the set of those who opted for Math = 120/7 = 17.

The 10th, 20th, 30th….. numbered students would have opted for both Physics and Chemistry.
Therefore, A n B = 120/10 = 12

The 14th, 28th, 42nd….. Numbered students would have opted for Physics and Math.
Therefore, C n A = 120/14 = 8

The 35th, 70th…. numbered students would have opted for Chemistry and Math.
Therefore, B n C = 120/35 = 3

And the 70th numbered student would have opted for all three subjects.

Therefore, AUBUC = 60 + 24 + 17 – (12 + 8 + 3) + 1 = 79.

Number of students who opted for none of the three subjects = 120 – 79 = 41.

Shortcut for this question.
Solve this via probability:
Total 120
Not multiple of two 1/2
Not multiple of five 4/5
Not multiple of seven 6/7

So total numbers who opt for none of the three subjects
120 x 1/2 x 4/5 x 6/7 = 41

Scope and syllabus for Set theory in CAT, CMAT, NMAT, SNAP and other entrance exams:

  • Basics
  • Two parties Normal Venn
  • Two parties 3D venn (CAT, CMAT)
  • Two parties Maxima Minima
  • Three parties Normal Venn
  • Three parties Maxima Minima
  • Four parties
Importance in Set theory in CAT, CMAT, NMAT, SNAP and other entrance exams
Set theory in CAT – 1 – 2  questions
Set theory in CMAT – 2 – 3 questions
Set theory in NMAT – 3 questions
Set theory in CET – 1 question
Set theory in SNAP – 2 ques
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