# GATE2015 CE-2: GA-10

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There are $16$ teachers who can teach Thermodynamics $\text{(TD)}$, $11$ who can teach Electrical Sciences $\text{(ES)}$, and $5$ who can teach both $\text{TD}$ and Engineering Mechanics $\text{(EM)}$. There are a total of $40$ teachers. $6$ cannot teach any of the three subjects, i.e. $\text{EM, ES}$ or $\text{TD}$. $6$ can teach only $\text{ES}$. $4$ can teach all three subjects, i.e. $\text{EM, ES}$ and $\text{TD}$. $4$ can teach $\text{ES}$ and $\text{TD}$. How many can teach both $\text{ES}$ and $\text{EM}$ but not $\text{TD}$?

1. $1$
2. $2$
3. $3$
4. $4$

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venn-diagram - A total of 11 teachers can teach ES.
Now the question says, 6 teachers can teach only ES so the number of teachers teaching both ES and EM has to be less than or equal to $(11-6)$ i.e., 5.

Also, 4 teachers can teach all three subjects.
The question asks for the number of teachers who can teach ES and EM but not TD.
Subtract $4$ from the $5$ derived earlier.

Ans 1. Option A

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