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how many students did not receive an A on the final exam?

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by himu » Wed Feb 13, 2013 9:21 pm
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
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105
135
180
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by mkdureja » Thu Feb 14, 2013 1:37 am
25% receive A in final exam
2/3rd of these = 50/3 % recieve A in class as a whole
Student receiving A on final exam but not in class = 1/3 rd of 25% = 25/3 % =15.
question asks, no. of students who didn't recieved A on final exam = 75%
So, if 25/3 % = 15
25% = 45
75% = 135 Ans.
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by hemant_rajput » Thu Feb 14, 2013 2:06 am
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

Total no. of students equal to x.

given 25% of x got A in final exam. 1/3 of these students who didn't received A's in the class as a whole, i.e. 15.

15 = (1/3 )*(25% of X)
15= (1/3)*(1/4) * X
so X equals to 180.

so students who did not receive an A on the final exam are 180 - (25 % of 180) =>180 - 45 = 135
I'm no expert, just trying to work on my skills. If I've made any mistakes please bear with me.
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by GMATGuruNY » Thu Feb 14, 2013 3:44 am
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 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.
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by ceilidh.erickson » Thu Feb 14, 2013 11:09 am
I find that these kinds of questions are best solved with an OVERLAPPING SETS MATRIX:

Image

Since we have fractions, percents, and real numbers given, we have to assign a variable for the total number of students, and fill in the rest accordingly. (It's best to work with all fractions, since 2/3 is a non-terminating decimal).

Image

When you have fractions or percents given, it's important to ask yourself - is this a portion of the total, or a portion of some category? Here, we're given that 2/3 of these students received A's in the class, so it's a portion of a category:

Image

If we know that 15 students got A's on the final but not in the class, then (1/3)(1/4)T = 15.

Image

If T = 180, then (3/4)T = 135. The answer is D.
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