A class took two tests, one in Physics and one in Math.

Question

A class took two tests, one in Physics and one in Math.
 
 1/4 of the students failed in Physics. 
 60% of those who passed Physics also passed Math. 
 If 300 students took both tests and 140 students passed exactly one of the two subjects,
 how many students failed in both subjects?

A. 100
B. 75
C. 50
D. 25
E. 0

stne · Answer

Please refer to the attached image:

https://i.postimg.cc/4dTyH77J/Screenshot-2025-12-23-115933.png

We know   a +b= 140

135 +a +b+x=300

135 +140 +x= 300

x=25

Ans D

Hope it helped.

WiziusCareers1 · Answer

1. Determine Physics results 
Total students: 300.
Failed Physics: (1/4) * 300 = 75 students.
Passed Physics: 300 − 75 = 225 students.

2. Determine Math results for those who passed Physics 
Passed both Physics and Math: 60% of those who passed Physics = 0.60 × 225 = 135 students.
Passed Physics but failed Math: 225 − 135 = 90 students.

3. Analyze the "Exactly One Subject" constraint The problem states that 140 students passed exactly one subject. This group consists of two sub-groups: 
Those who passed Physics but failed Math (already calculated as 90).
Those who passed Math but failed Physics.
Passed Math but failed Physics: 140 − 90 = 50 students.

4. Final Calculation: Failed in both subjects We know that a total of 75 students failed Physics. These 75 students are split into two groups: 
Those who failed Physics but passed Math (calculated as 50).
Those who failed both Physics and Math.
Failed both subjects: 75 − 50 = 25 students.

gullyboy09 · Answer

If 300 students took both tests... -> This line is confusing, IMO it indicates that there might be students who wrote only one test, and there is no way to solve this then. In general I find questions from Expert Global not so very well written.

ExpertsGlobal5 · Answer

Hello,

In the context of overlapping sets, and even in general,  “both” simply and always means “both A and B” . Navigating such vocabulary is a part of the challenge called GMAT.

For end-to-end, free coverage of Overlapping Sets for GMAT, please refer to the following page; it will take you through all the concepts in a progressive manner and give you adequate practice for all variations:

https://www.expertsglobal.com/gmat-overlapping-sets-prep-venn-diagram-line-diagram/

Hope that helps.

All the best!
Experts' Global

gullyboy09 · Answer

I got both means both A and B. But if the problem says "a class took two tests" but specifies that  300 took both tests , it implies there could be other students in the class who only took  one  of the tests (or maybe neither).

FreshStove · Answer

Doesn't "60% of those who passed physics, also passed Math" mean that 60% of those who only passed Physics?

Bunuel · Answer

No. “60% of those who passed Physics also passed Math” means 60% of all students who passed Physics.

So first take everyone who passed Physics. Then, from that group, 60% also passed Math.

“Passed Physics” does not mean “passed Physics only.”

KarishmaB · Answer

300 took the tests.
140 passed in exactly one subject. 
3/4th of 300 i.e. 225 passed in physics and 60% of these i.e. 135 passed Math also. So this means that 135 passed both the tests.

So out of 300, 140 passed in exactly one subject and 135 passed in both subjects. This means 300 - 140 - 135 = 25 passed in neither subject

Answer (D)

A class took two tests, one in Physics and one in Math.

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A class took two tests, one in Physics and one in Math.

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