himu wrote: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 whole class OR didn't.
For an EITHER/OR group problem, use a GROUP GRID (also known as a double-matrix) to organize the data.
Let AF = A on the final, NF = not A on the final, AC = A for the whole class, and NC = not A 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:
Now let's use the information in the question stem to complete as much of the grid as possible.
Values in the grid must 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, the following grid is yielded:
2/3 of these students received A's in the class as a whole.
Since (2/3)(3x) = 2x, the following grid is yielded:
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.
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