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by j_shreyans » Sun Nov 02, 2014 9:47 am
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

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by [email protected] » Sun Nov 02, 2014 10:29 am
Hi j_shreyans,

This question is essentially just a big algebra question, although it can be solved in other ways. You have to be careful to answer the question that is ASKED though.

We have a class in which 25% of the students received As on the final exam:

X = Total students in class
.25X = students who received an A on the final

2/3 of the students of THESE students (the ones who received an A on the final) received As in the class as a whole:

.25X = students who received an A on the final
.25X(2/3) = also got an A in the class as a whole
.25X(1/3) = did NOT get an A in the class as a whole

15 students received As on the final but did NOT get an A in the class:

15 = .25X(1/3)

so....

30 = .25X(2/3)

45 = .25X

180 = X = total number of students in the class

How many students did NOT receive an A on the FINAL?

25% DID receive an A, so 75% did NOT receive an A:

(.75)(180) = 135

Final Answer: D

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by GMATGuruNY » Sun Nov 02, 2014 12:52 pm
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:
Image

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:
Image

2/3 of these students received A's in the class as a whole.
Since (2/3)(3x) = 2x, the following grid is yielded:
Image

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 Brent@GMATPrepNow » Sun Nov 02, 2014 12:58 pm
I'd like to point out that Mitch's "group grid" approach (aka the Double Matrix Method)can be used for most questions featuring a population in which each member has two characteristics associated with it.
Here, we have a population of students, and the two characteristics are:
- receive an A in the class or did not receive an A in the class
- received an A on the final exam or did not receive an A on the final exam

This question type is VERY COMMON on the GMAT, so be sure to master the technique.

To learn more about the Double Matrix Method, watch our free video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

Once you're familiar with this technique, you can attempt these additional practice questions:

Easy Problem Solving questions
- https://www.beatthegmat.com/the-aam-aadm ... 72242.html
- https://www.beatthegmat.com/finance-majo ... 67425.html

Medium Problem Solving questions
- https://www.beatthegmat.com/probability- ... 73360.html
- https://www.beatthegmat.com/posted-speed ... 72374.html
- https://www.beatthegmat.com/motel-t271938.html
- https://www.beatthegmat.com/of-the-appli ... 70255.html
- https://www.beatthegmat.com/opening-nigh ... 64869.html
- https://www.beatthegmat.com/ds-french-ja ... 22297.html
- https://www.beatthegmat.com/prblem-solving-t279424.html

Difficult Problem Solving questions
- https://www.beatthegmat.com/ratio-problem-t268339.html
- https://www.beatthegmat.com/overlapping- ... 65223.html
- https://www.beatthegmat.com/fractions-t264254.html
- https://www.beatthegmat.com/overlapping- ... 64092.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-2

Easy Data Sufficiency questions
- https://www.beatthegmat.com/for-what-per ... 70596.html
- https://www.beatthegmat.com/ds-quest-t187706.html

Medium Data Sufficiency questions
- https://www.beatthegmat.com/sets-matrix-ds-t271914.html
- https://www.beatthegmat.com/each-of-peop ... 71375.html
- https://www.beatthegmat.com/a-manufacturer-t270331.html
- https://www.beatthegmat.com/in-costume-f ... 69355.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-1

Difficult Data Sufficiency questions
- https://www.beatthegmat.com/double-set-m ... 71423.html
- https://www.beatthegmat.com/sets-t269449.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-3

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Mathsbuddy » Mon Nov 03, 2014 9:24 am
This does not provide the right answer. Can anyone try to see what I'm doing and why it is incorrect?
Thanks.

C = no. in class
C/4 scored A in finals
(C-d)/4 = 15, so d = C - 60 where d = no. who scored A in class, but not in finals

2/3*C/4 = 3C/2 scored A in finals and/or other exams
3C/2-C/4 = 5C/4 scored A in other exams only = d

So 5C/4 = C - 60
5C = 4C - 240
C = 240

d = 240-60 = 180
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