The political science departments at a university surveyed a number of politicia

Question

The political science departments at a university surveyed a number of politicians regarding their perception of college students and gathered the following information:

a. 15 saw students as hardworking and economically advantaged

b. 25 saw students as hardworking. (Hint:some of the 25 are economically advantaged and some are not)

c. 11 believed students were economically advantaged but not hardworking.

d. 16 believed students were neither hardworking nor economically advantaged.

How many politicans were surveyed?

Explanation / Answer

Let the left circle represent those who said they were hardworking (H). Let the right circle represent those who said they were advantaged (A). Then, the intersection of these represents those who said they were BOTH. By part (a), this is 15. Part (b) says that 25 said they were hardworking, so the left circle must have 25 in it TOTAL. 15 is already in the intersection of H and A, so that leaves 10 outside of it. [In the left circle, but NOT in the intersection.] Part (c) says that 11 said they were A but not H. This is exactly the right circle OUTSIDE of the intersection. So far we have: 10 in H alone, 15 in H and A, 11 in A alone. Finally, part (d) says that 16 are NEITHER H nor A. This is represented by the area in the rectangle outside of the circles. The total number surveyed can be found by adding up those that said they were: H alone, H AND A, A alone, and NEITHER These numbers are 10 + 15 + 11 + 16 = 52.

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