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by GMATGuruNY » Mon Dec 02, 2013 5:01 am
----------------YES---------NO----UNSURE
Subject M--------500--------200-----100
Subject R--------400--------100-----300


A total of 800 students were asked whether they found two subjects, M and R, interesting. Each answer was either "yes" or "no" or "unsure", and the numbers of students who gave these answers are listed in the table above. If 200 students answered "yes" only for subject M, how many of the students did not answer "yes" for either subject?

A. 100
B. 200
C. 300
D. 400
E. 500
Use a Venn diagram to represent all of the YES voters:

Image

The TOTAL who voted YES for M = 500.
The number who voted YES for ONLY M = 200.
Thus, the number who voted YES for BOTH M AND R = 300.

Since the TOTAL number who voted YES for R=400, and 300 of these people voted YES for BOTH M AND R, the number who voted YES for ONLY R = 400-300 = 100.

Adding the values in the Venn diagram, we get:
Total number of YES voters = 200+300+100 = 600.

Since the total number of voters = 800, and the total number of YES voters = 600, the number who did NOT vote YES = 800-600 = 200.

The correct answer is B.
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by Mathsbuddy » Mon Dec 02, 2013 9:14 am
Drawing a Venn diagram for Yes:
M only = 200, M intersect R = 300, R only = 100

Drawing a Venn diagram for No:
M only = 100, M intersect R = 100, R only = 0
100 + 100 = 200

Check: total = 200 + 300 + 100 + 100 + 100 = 800 OK :)

Answer B) 200.

Note that the intersections of 300 and 100 match the UNSURE figures, because the interections are in fact just that.
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