There are 36 teachers in a school. There are 11 who can teach Thermodynamics (TD), 5 who can teach Electrical Sciences (ES), and 5 who can teach Engineering Mechanics (EM). There are a total of 36 teachers. 4 cannot teach any of the three subjects. 6 can teach only ES. 4 can teach all three subjects, i.e., TD, ES and TD. 4 can teach TD and ES but NOT EM. How many teachers can teach only TD? A. 0 B. 2 C. 3 D. 4

GATE 2015 · General Aptitude · Venn Diagram · medium

Answer: 0 teachers can teach only Thermodynamics (TD).

1. Identify known intersection regions involving TD: 11 = only_TD + 4 (TD and ES, not EM) + |TD intersect EM only| + 4 (all three)
2. Use total teachers in active subjects = 32: only_TD + only_ES + only_EM + |TDnES| + |TDnEM| + |ESnEM| + |all three| = 32. Given: only_ES=6, |TDnES only|=4, |all three|=4. Remaining: only_TD + only_EM + |TDnEM only| + |ESnEM only| = 32 - 6 - 4 - 4 = 18.
3. Conclude: teachers who teach only TD: With |TD|=11, |TDnES only|=4, |TDnEM only|=3, |all three|=4: only_TD = 11 - 4 - 3 - 4 = 0.