GO Classes Test Series 2024 | Mock GATE | Test 14 | Question: 7

Question

A class of 30 students was asked what they did on their winter holiday. 20 students said that they went skating. 9 students said that they went skiing. Exactly 5 students said that they went skating and went skiing. How many students did not go skating and did not go skiing?

• A. 1
• B. 6
• C. 11
• D. 19

Comments

Total(S) = 30

Skating = 20

Skiing = 9

Skating AND Skiing = 5

We need to find (Not Skating AND Not Skiing) = (A OR B)'

We know A' AND B' = (A OR B)'

A OR B = A + B - A AND B = 20 + 9 - 5 = 24

(A OR B)' = 30-24 = 6

Answer 1

Since 20 students went skating and 5 students went both skating and skiing, then 20 − 5 = 15 students went skating only. Since 9 students went skiing and 5 students went both skating and skiing, then 9 − 5 = 4 students went skiing only. The number of students who went skating or skiing or both equals the sum of the number who went skating only, the number who went skiing only, and the number who went both skating and skiing, or 15 + 4 + 5 = 24. Therefore, 30 − 24 = 6 students did not go skating or skiing.