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In a certain class of students, 25% received A’s on the final exam and
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01 Apr 2021, 06:30
01 Apr 2021, 06:30
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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
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 final exam and
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02 Apr 2021, 08:10
02 Apr 2021, 08:10
GeminiHeat 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
A. 45
B. 60
C. 105
D. 135
E. 180
Let the total number of students in the class be \(x\)
Students with A \(= 0.25x\)
Students with not an A \(= 0.75x\)
Now, Students with an A in the class \(= \frac{2}{3}(0.25x)\)
So, Students with not an A in the class \(= \frac{1}{3}(0.25x) = 15\)
\(0.25x = 45\)
\(x = 180\)
Therefore, Students with not an A \(= 0.75x = 0.75(180) = 135\)
Hence, option D
Re: In a certain class of students, 25% received A’s on the final exam and
[#permalink]
04 Apr 2021, 05:29
04 Apr 2021, 05:29
1
Here,
Since, \(\frac{2}{3} \) of students received A in the class as whole, so \(\frac{1}{3}\) of students received A in final but not in class as whole and they are = 15 students
25 % received A on final exam
Let the total number of student = x
we can re-write the equation as -
\( \frac{1}{4 }* \frac{1}{3} * x = 15 \)
or \(x = 180\)
Since 25% received A , therefore 75% didnot received A ,
i.e = \(\frac{3}{4}\) * 180 = 135
SECOND METHOD: -
Let pick an answer from the given answer, (we can start for C or D and move up or down accordingly)
Let us choose C, which is = 105 ( total number of students didn't received A)
i.e \(\frac{3}{4 } x = 105 \)
or \(x = 140 \)
25% of 140 = 35
and \( \frac{2}{3 } * 35 = \frac{70}{3}\)
check {\(35 - (\frac{75}{3}) \)} < 15 students , which donot match as per the information provided in question. Hence option C is not our answer ( also note 35 - 75/ 3 = almost 11, so we move down to option D)
so we need to move to option D, which is 135 students
now,
\(\frac{3}{4 } * x = 135\)
or x = 180
25% of 180 = 45
and \(\frac{2}{3} * 45 = 30\)
check 45 - 30 = 15 students students in the class received A’s on the final exam but did not receive an A in the class ( which is given )
Hence option D is our answer
Since, \(\frac{2}{3} \) of students received A in the class as whole, so \(\frac{1}{3}\) of students received A in final but not in class as whole and they are = 15 students
25 % received A on final exam
Let the total number of student = x
we can re-write the equation as -
\( \frac{1}{4 }* \frac{1}{3} * x = 15 \)
or \(x = 180\)
Since 25% received A , therefore 75% didnot received A ,
i.e = \(\frac{3}{4}\) * 180 = 135
SECOND METHOD: -
Let pick an answer from the given answer, (we can start for C or D and move up or down accordingly)
Let us choose C, which is = 105 ( total number of students didn't received A)
i.e \(\frac{3}{4 } x = 105 \)
or \(x = 140 \)
25% of 140 = 35
and \( \frac{2}{3 } * 35 = \frac{70}{3}\)
check {\(35 - (\frac{75}{3}) \)} < 15 students , which donot match as per the information provided in question. Hence option C is not our answer ( also note 35 - 75/ 3 = almost 11, so we move down to option D)
so we need to move to option D, which is 135 students
now,
\(\frac{3}{4 } * x = 135\)
or x = 180
25% of 180 = 45
and \(\frac{2}{3} * 45 = 30\)
check 45 - 30 = 15 students students in the class received A’s on the final exam but did not receive an A in the class ( which is given )
Hence option D is our answer
