Problem Solving

In a certain class of students, 25% received A's on the final exam and 2/3 of these students received A's in the class as a whole. If 15 students in the class received A's on the final exam but did not receive an A in the class, how many students did not receive an A on the final exam?
a 45
b 60
c 105
d 135
e 180

In a certain class of students, 25% received A's on the final exam and 2/3 of these students received A's in the class as a whole. If 15 students in the class received A's on the final exam but did not receive an A in the class, how many students did not receive an A on the final exam?
45
60
105
135
180

This is an EITHER/OR group question.
Every student EITHER received an A on the final OR didn't.
Every student EITHER received an A for the course OR didn't.
For an EITHER/OR group problem, use a GROUP GRID to organize the data.

Let YF = yes on the final, NF = no on the final, YC = yes for the whole class, and NC = no for the whole class.
There are two fractions in the question stem: 25%=1/4 and 2/3.
Since the product of the denominators = 4*3 = 12, let the TOTAL = 12x.
Here's the grid:

_______________YF______NF_______Total

YC:

NC:

Total:___________________________12x

Now let's use the information in the question stem to complete as much of the grid as possible.
Values in the grid have to add up horizontally and vertically.
As soon as we know 2 entries in a row or a column, we can calculate the remaining entry in that row or column.

25% received A's on the final exam:
Since (1/4)(12x) = 3x, we get:

_______________YF______NF_______Total

YC:

NC:

Total:__________3x______9x_______12x

2/3 of these students received A's in the class as a whole.
Since (2/3)(3x) = 2x, we get:

_______________YF______NF_______Total

YC:____________2x_______________

NC:____________x_________________

Total:__________3x______9x_______12x

15 students in the class received A's on the final exam but did not receive an A in the class.
In the grid above, this is the value of x.
Thus, x=15, implying that the total number of students who did not receive an A on the final = 9x = 9*15 = 135.

The correct answer is D.