In an examination 43% passed in Math, 52% passed in Physics and 52%

Question

In an examination 43% passed in Math, 52% passed in Physics and 52% passed in Chemistry. Only 8% students passed in all the three. 14% passed in Math and Physics and 21% passed in Math and Chemistry and 20% passed in Physics and Chemistry. Number of students who took the exam is 200. Let Set P, Set C and Set M denotes the students who passed in Physics, Chemistry and Math respectively. Then How many students passed in Math only?

A. 32
B. 42
C. 45
D. 52
E. 56

A. 32
B. 42
C. 45
D. 52
E. 56

gmatophobia · Answer

We can plot the information on a Venn diagram as shown below - Screenshot 2023-05-24 041906.jpg Only Math = 16% \frac{16}{100} * 200 = 32 Option A

AndrewN · Answer

I have to say that the sentence about assigning variables to the three classes seems un-GMAT™-like, but hey, I am (mostly) a rule respecter, so I used a Venn Diagram method similar to the one in the post above, only I converted all the percentages to students upfront. Screen Shot 2023-05-23 at 19.29.28.png To solve this type of overlapping sets question, make sure there are no people who fall outside the target regions . In this particular question, we are told that 200 students took the exam , so we must be working with all 200 students. Another question might tell you that, say, 10% of students were absent, and you would have to remove these students from consideration. Once you have removed any non-participants, work from the center, the green region, first if possible to avoid extra counting later. If 8% passed all subjects, then there are 16 students in this region. Next, write in as much information about the other areas of overlap, the blue regions above, being careful not to count the students already in the center. If 14% passed in Math and Physics , then 28 students passed both. However, 16 of these students were already counted , so only 12 remain. Then, if 21% passed in Math and Chemistry , 42 students passed both. Again, 16 of these students were already counted , so only 26 remain. Finally, if 20% passed in Physics and Chemistry , then 40 students passed both, and by now, we ought to know that 24 passed these two subjects without passing Math. Finally, since we are not interested in any remaining area other than the students passed in Math only , we can turn our attention to the orange region. If 43% passed in Math , then 86 students passed, and we can subtract the other areas within the Math circle that have already been filled out to get our answer, as shown above. If you wanted to make sure your answer was correct, you could quickly figure out the numbers for the other missing areas and add everything up. If the sum was 200, you would have to be correct. I know there is a formula you can memorize to solve these questions, but in general, I find an analytical and organized approach much more intuitive and much less error-prone. Good luck with your studies. - Andrew

MBAHOUSE · Answer

In an examination 43% passed in Math, 52% passed in Physics and 52% passed in Chemistry. Only 8% students passed in all the three. 14% passed in Math and Physics and 21% passed in Math and Chemistry and 20% passed in Physics and Chemistry. Number of students who took the exam is 200. Let Set P, Set C and Set M denotes the students who passed in Physics, Chemistry and Math respectively. Then How many students passed in Math only?

A. 32
B. 42
C. 45
D. 52
E. 56

In an examination 43% passed in Math, 52% passed in Physics and 52%

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In an examination 43% passed in Math, 52% passed in Physics and 52%

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