A class was tested on two subjects-Mathematics and Physics. 80% of the students passed in Mathematics.

[Gmat_mission]

A class was tested on two subjects-Mathematics and Physics. 80% of the students passed in Mathematics. This number was 120 more than the number of students who passed in Physics. If 180 students passed in both the subjects and the ratio of students who passed only in Physics and only in Mathematics was 1:7, how many students passed in neither of the two subjects?

A. 40
B. 50
C. 60
D. 70
E. 80

Answer: C

Source: e-GMAT

[Scott@TargetTestPrep]

A class was tested on two subjects-Mathematics and Physics. 80% of the students passed in Mathematics. This number was 120 more than the number of students who passed in Physics. If 180 students passed in both the subjects and the ratio of students who passed only in Physics and only in Mathematics was 1:7, how many students passed in neither of the two subjects?

A. 40
B. 50
C. 60
D. 70
E. 80

Answer: C

Solution:

We can let x = the total number of students. Therefore, 0.8x students passed in Mathematics and 0.8x - 120 students passed in Physics.

Since 180 students passed in both subjects, we have 0.8x - 180 students passed only in Mathematics and 0.8x - 120 - 180 = 0.8x - 300 students passed only in Physics. Since the ratio of students who passed only in Physics and only in Mathematics was 1:7, we can create the proportion:

(0.8x - 300) / (0.8x - 180) = 1/7

5.6x - 2100 = 0.8x - 180

4.8x = 1920

x = 400

We see that there are 400 students in the class, so 0.8(400) = 320 students passed in Mathematics and 320 - 120 = 200 students passed in Physics. To find the number of students who passed in neither subject, we can use the formula:

Total = Math + Physics - Both + Neither

400 = 320 + 200 - 180 + Neither

400 = 340 + Neither

60 = Neither

Answer: C