Problem Solving

In a certain school, 40 more than 1/3 of all the students are taking a science course and 1/4 of those taking a science course are taking physics. If 1/8 of all the students in the school are taking physics, how many students are in the school?

A) 240

B) 300

C) 480

D) 720

E) 960

The solution below is taken from the GMATFix App.



-Patrick

GmatGreen wrote:In a certain school, 40 more than 1/3 of all the students are taking a science course and 1/4 of those taking a science course are taking physics. If 1/8 of all the students in the school are taking physics, how many students are in the school?

A) 240

B) 300

C) 480

D) 720

E) 960

We can PLUG IN THE ANSWERS, which represent the total number of students.
Since 1/8 of the students take physics, the correct answer choice must be a multiple of 8.
Eliminate B.

C: 480
Since 1/8 of the students take physics, students taking physics = (1/8)(480) = 60.
Since 40 more than 1/3 of the students take science, students taking science = 40 + (1/3)(480) = 200.
Since 1/4 of the science students take physics, we get:
Students taking physics = (1/4)(200) = 50.
Doesn't work: the values in red differ by 10.

Let's try a greater answer choice.

D: 720
Since 1/8 of the students take physics, students taking physics = (1/8)(720) = 90.
Since 40 more than 1/3 of the students take science, students taking science = 40 + (1/3)(720) = 280.
Since 1/4 of the science students take physics, we get:
Students taking physics = (1/4)(280) = 70.
Doesn't work: the values in red differ by 20.

Plugging in a greater answer choice INCREASES the difference between the values in red.
Thus, the correct answer choice must be LESS than the value in C.

The correct answer is A.