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