I am taking a short cut here by adding the numbers in the region that fall inside the three circles. You could add each region individually in the following manner:

$$100 = (40 – a – b – d) + (a + b + c + d ) + (75-a-d-c) + (30-b-d-c)$$

You will notice that the first two terms in the parentheses add up to $40+c$, this was the short cut I took in the explanation.

Grant says

At 2:45, why is that entire region 40, and the equation that represents it is 40-c? Why would it not be 40-a-d-b like the other two sections?

Grant says

40+c *

Akshit says

Because he is trying to calculate value of D

GMAT Quantum says

I am taking a short cut here by adding the numbers in the region that fall inside the three circles. You could add each region individually in the following manner:

$$100 = (40 – a – b – d) + (a + b + c + d ) + (75-a-d-c) + (30-b-d-c)$$

You will notice that the first two terms in the parentheses add up to $40+c$, this was the short cut I took in the explanation.

I hope this makes sense.

M says

Thanks for explaining, it was confusing.