JEE Main 2020 · 5 September · morning · Single correct · +4 / −1
A survey shows that 73% of the persons working in an office like coffee, whereas 65% like tea. If x denotes the percentage of them, who like both coffee and tea, then x cannot be :
- (a) 63
- (b) 36
- (c) 54
- (d) 38
Answer and solution
Answer (b) 36
Solution
Maths sir · 3 steps
Squeeze the overlap from both sides: at least 73 + 65 - 100, at most the smaller of 73 and 65.
- Lower bound. By the addition theorem, n(C ∪ T) = 73 + 65 - x = 138 - x. A percentage cannot exceed 100, so 138 - x ≤ 100, which gives x ≥ 38.
- Upper bound. The people who like both are part of the tea group, and only 65% like tea. So x ≤ 65.
38 ≤ x ≤ 65
- So. 63, 54 and 38 all lie in this range, but 36 is below 38. The value x cannot take is 36, option (b).
The idea to keep. For two overlapping groups, the overlap is at least P(A) + P(B) - 100% and at most the smaller of the two. Check every option against both bounds.
Answer from the NTA final answer key. Solution by PrepWiser.