Which Number Produces An Irrational Number When Ad - Gauthmath

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Step 1: Draw three overlapping circles representing Nepali ($N$), English ($E$), and Maths ($M$). Since all students who study English also study Nepali, the circle for $E$ is entirely contained within the circle for $N$.

Step 2: The number of students who study all three subjects is 3. This goes in the intersection of all three circles.

Step 3: The number of students who study only Nepali is 4. This goes in the region of the Nepali circle that does not overlap with the English or Maths circles.

Step 4: The number of students who study English is 8. Since the English circle is inside the Nepali circle and 3 students study all three subjects, the number of students who study English and Nepali and Maths is 3. The number of students who study English and Nepali only is $8 - 3 = 5$.

Step 5: The number of students who study Nepali is 14. We know that 4 study only Nepali, 5 study Nepali and English only, and 3 study all three subjects. Therefore, the number of students who study Nepali and Maths only is $14 - 4 - 5 - 3 = 2$.

Step 6: The total number of students is 20. We have accounted for $4 + 5 + 3 + 2 = 14$ students. The remaining students study only Maths. Thus, the number of students who study only Maths is $20 - 14 = 6$.

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