Bunuel wrote:
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
One approach is to use the
Double Matrix Method. This technique can be used for questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions).
Here, we have a population of students, and the two characteristics are:
- passed math for didn't pass math
- passed physics or didn't pass physics
Aside: We can also use Venn diagrams and formulae to solve overlapping sets questions. However, as difficulty levels increase, it becomes harder to apply those other approaches, whereas the Double Matrix Method works every time. Given: 80% of the students passed MathematicsSo, if we let x = the total number of students, then
0.8x = the total number of students that passed mathematics.
If 80% of the students passed mathematics, then 20% of the x students failed.
So,
0.2x = the total number of students that failed mathematics.
So, we can set up our Matrix as follows:
Given: The number of students who passed Mathematics is 120 more than the number of students who passed in Physics.In other words, the number of students who passed physics is
120 less than the number of students who passed math.
So, the number of students who passed physics =
0.8x - 120If there are
x students in total, and
0.8x - 120 of them passed physics, then the number of students who failed physics =
x -
(0.8x - 120) = 0.2x + 120So, we have:
Given: 180 students passed in both subjects.So, we have:
At this point we can populate the remaining boxes.
Since the two TOP boxes must add to
0.8x, the top right box
= 0.8x - 180.
Since the two boxes on the LEFT side must add to
0.8x - 120, the bottom left box
= (0.8x - 120) - 180 = 0.8x - 300.
Since the two BOTTOM boxes must add to
0.2x, the bottom right box
= 0.2x - (0.8x - 300) = 300 - 0.6x.
So we have:
Given: The ratio of students who passed only in Physics and only in Mathematics was 1:7So we get the following equation:
(0.8x - 300)/(0.8x - 180) = 1/7Cross multiply to get:
5.6x - 2100 = 0.8x - 180Rearrange to get:
4.8x = 1920Solve:
x = 400We know that the number of students who failed both courses =
300 - 0.6x,
Plug in x = 400 to get:
300 - 0.6(400) = 300 - 240 = 60Answer: C
This question type is
VERY COMMON on the GMAT, so be sure to master the technique.
To learn more about the Double Matrix Method, watch this video:
EXTRA PRACTICE QUESTION
More questions to practice with:
EASY:
https://gmatclub.com/forum/of-the-120-p ... 15386.html MEDIUM:
https://gmatclub.com/forum/in-a-certain ... 21716.html HARD:
https://gmatclub.com/forum/a-group-of-2 ... 24888.html KILLER:
https://gmatclub.com/forum/a-certain-hi ... 32899.html