In a certain class of students, 25% received A’s on the fina

Question

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

A. 45
B. 60
C. 105
D. 135
E. 180

SruGan · Accepted Answer

Here's another way to do using double-matrix method:

Zarrolou · Answer

This question has a complicated text, lets try to semplify it.

25% received A’s on the final exam and 2/3 of these students received A’s in the class as a whole

25%  A in final =>  25%*\frac{2}{3} =overall A -  25%*\frac{1}{3} =No overall A

If 15 students in the class received A’s on the final exam but did not receive an A in the class

Now this portion refers to the expression  25%*\frac{1}{3}  (A in final but no overall) so  25%*\frac{1}{3}=15

With that expression we know that 25%*1/3 of the students equals 15. so 25% of the students are 25%*(1/3)*3=15*3

25%=15*3=45

Number of students= 180

how many students did not receive an A on the final exam?  (25% received A’s)

180*\frac{3}{4}=135  or even better  180-45=135

D

pikachu · Answer

Finally after hammering through the confusing text and spending a ton of time :cry:

I was able to figure out an easy way to solve this problem by using the matrix approach. Lets set up a matrix as in the attachment: Since the problem involves a fraction 2/3 and a percent 25%, the best way to move forward is to convert the 25% into a fraction = 1/4. Note the denominator of the two fractions would be 1/3*1/4 = 1/12. So let the total number of students in the class be 12x. Hence the number of students who got an A on the final exam would be 3x (as we are told that 25% of the total population received an A on the final exam). We also know that the number of students who did get an A on the final exam but did not get an A in the class = 15 = x. So we can simply use this knowledge to calculate 9x = 15*9 = 135. Answer D.

mau5 · Answer

Let the total no of students in the class be S. Now, S/4 = 'A' on final exam--> 2/3rd = S/6 = Received A's in the class.Thus, students who received A's only on the final exam = 1/3*S/4 = S/12--> S/12 = 15 or S = 180. Thus, Students not receiving A on the final exam = 3/4*S = 45*3 = 135.

D.

One can also eliminate options B,C immediately after reading the question.

pikachu · Answer

Hi vinaymimani,

"One can also eliminate options B,C immediately after reading the question" can you please elaborate how. This is one thing I struggle with is eliminating the wrong answer choices. Any suggestions.

mau5 · Answer

Sure. We know that 25% received A on the final exam. Thus, those who didn't receive A on the final exam = 75% = 3/4*S, where S is the no of students in the class.
Thus, S/4 = 25% of S = The no of people who received A on the final exam = one of the options/3 = Options/3. Now, again, 2/3rd of THESE many students received A in the calss as whole --> 2*option/9 = Integer. Options B and C are not divisible by 9. The remaining three are. Hope this clears your doubt.

DensetsuNo · Answer

Answer\; =\; \frac{75*45}{25}\; =\; 135\;

15\; =>\; \frac{1}{3},\; \frac{3}{3}\; =\; 45,

45=\; 25 %  \; of \; total

100-25=\; 75

45:25=x:75

\frac{75*45}{25}\; =\; 135

Answer\; D\;

SeregaP · Answer

try to write what is asked in the beginning, that's why I failed this question

I tried grid as presented above and got to the point 15=1/12
question asks what is 3/4 or 9/12=>15*9=135

EMPOWERgmatRichC · Answer

Hi All,

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

GMAT assassins aren't born, they're made, 
Rich

DharLog · Answer

1/4 - received A on the final exam
3/4 - did not receive A on the final exam
1/4 * 2/3 = 1/6 - received A in the class as the whole
1/4 - 1/6 = 1/12 - received A on the final exam, but not the whole

So,
1/12 - 15 students
3/4 - ?

3/4 = 9 * 1/12 = 9 * 15 = 135
Option D

ScottTargetTestPrep · Answer

We can let x = the number of students in the class.

Since ⅔ of the students who received A’s in the final also received A’s in the class as a whole, ⅓ of the students received A’s in the final but did not receive A’s in the class as a whole, and we are given that there are 15 such students. So we have:

(⅓)(¼)(x) = 15

x/12 = 15

x = 180

Since 25%, or ¼, of the students in the class received A’s on the final, ¾ of 180 students, or 135 students, did not receive A’s on the final.

Answer: D,

carouselambra · Answer

This is for the folks not aware of the matrix method.

Assume the number of students as 120x (since it is divisible by 3 and 4)
Given, 25% got A, so 1/4(120)= 30x received 'A' 
Out of which, 20x received 'A' in class.

Now, if 15 students in the class received A’s on the final exam but did not receive an A in the class -
this means 10x =15, x=3/2

90x (120x-30x) did not receive 'A' at all.
So, 90(3/2) = 135

IMO D

bumpbot · Answer

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In a certain class of students, 25% received A’s on the fina

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