In an engineering college of 20,000 students, 1,500 like neither their core branches nor other branches. The number of s...

Question

In an engineering college of 20,000 students, 1,500 like neither their core branches nor other branches. The number of students who like their core branches is 1/4th of the number of students who like other branches. The number of students who like both their core and other branches is 500. The number of students who like only their core branches is

A. 3,300  B. 3,500  C. 1,600  D. 1,500

Accepted Answer

3,300 students like only their core branches. We have a two-set Venn diagram: Set C (core branches) and Set O (other branches) inside a universe of 20,000 students. We know how many are outside both sets (1,500), how many are in the overlap (500), and the ratio of total-core to total-other (1:4). Using inclusion-exclusion we find the size of each set, then subtract the overlap to get the 'only core' count.