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

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

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22 May 2013, 13:28
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55% (hard)

Question Stats:

67% (02:19) correct 33% (02:54) wrong based on 408 sessions

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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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Re: In a certain class of students, 25% received A’s on the fina  [#permalink]

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23 Jul 2016, 10:45
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Here's another way to do using double-matrix method:
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##### General Discussion
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Re: In a certain class of students  [#permalink]

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22 May 2013, 13:43
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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
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Re: In a certain class of students  [#permalink]

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22 May 2013, 15:55
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pikachu 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?
A. 45
B. 60
C. 105
D. 135
E. 180

Finally after hammering through the confusing text and spending a ton of time 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.
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Re: In a certain class of students  [#permalink]

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23 May 2013, 00:37
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pikachu 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?
A. 45
B. 60
C. 105
D. 135
E. 180

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.
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Re: In a certain class of students  [#permalink]

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23 May 2013, 08:22
vinaymimani wrote:
pikachu 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?
A. 45
B. 60
C. 105
D. 135
E. 180

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.

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.
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Re: In a certain class of students  [#permalink]

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23 May 2013, 09:34
pikachu wrote:
vinaymimani wrote:
pikachu 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?
A. 45
B. 60
C. 105
D. 135
E. 180

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

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.

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.
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In a certain class of students, 25% received A’s on the fina  [#permalink]

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23 Jul 2016, 18:04
$$Answer\; =\; \frac{75*45}{25}\; =\; 135\;$$

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

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

$$100-25=\; 75$$

$$45:25=x:75$$

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

$$Answer\; D\;$$
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Re: In a certain class of students, 25% received A’s on the fina  [#permalink]

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20 Mar 2017, 15:50
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
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Re: In a certain class of students, 25% received A’s on the fina  [#permalink]

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01 Mar 2018, 20:57
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

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Re: In a certain class of students, 25% received A’s on the fina  [#permalink]

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01 Aug 2018, 13:28
pikachu 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?

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

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
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Re: In a certain class of students, 25% received A’s on the fina  [#permalink]

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10 Aug 2018, 18:35
pikachu 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?

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

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.

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Re: In a certain class of students, 25% received A’s on the fina   [#permalink] 10 Aug 2018, 18:35
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