What is the approach I should take to solve these? I initally wanted to substitute a number for (like 100) N but it didn't work

In a nation wide poll, N people were interviewed. if 25% of them answered "yes" to Question 1, and of those, 33% answered Yes to Question 2.
Which of the following expresssions would represent the number of people interviewed who did not answer "yes" to both?

a N/7

b. 6N/7

c. 5N/12

d 7N/12

e 11N/12

Plugging in a number will work here but you have to make sure it's a number that will work "nicely" in the problem.

Also, the original problem does not give the numbers as 25% and 33% but as 1/4 and 1/3. This is important to note for two reasons: first, 33% is not the same number as 1/3 - close, but not the same. Second, the fact that the original problem is written in fractions gives you the clue as to what number to pick. You pick the common denominator - in this case, 4*3 = 12 - because then the numbers in the problem will work nicely.

N = 12
1/4, or 3, answer Yes to Q1. Therefore 9 answer No to Q1
1/3 of the 3, or 1, answers Yes to Q2. Therefore, 2 of the 3 answer No to Q2.

The number of people who answered Yes to both is 1. Therefore, the number of people who did NOT answer yes to both is 12-1 = 11.

Test N=12 in the answers and find the one that equals 11. Only E works.

_________________
Stacey Koprince
Instructor
Director of Online Community
ManhattanGMAT

it is using VIC and choosing a denominator that works for each fraction...thanks