**Question: **

Each of 74 students in a class studies at least one of the three subjects H, E and P. Ten students study all three subjects, while twenty study H and E, but not P. Every student who studies P also studies H or E or both. If the number of students studying H equals that studying E, then the number of students studying H is

**Show Answer**

Correct Answer: 52

Let the number of students who studying only H be h, only E be e, only H and P but not E be x, only E and P but not H be y

Given only P = 0 All three = 10; Studying only H and E but not P = 20

Given number of students studying H = Number of students studying E

= h + x + 20 + 10

= e + y + 20 + 10

h + x = e + y total number of students = 74

Therefore, h + x + 20 + 10 + e + y = 74

h + x + e + y = 44

h + x + h + x = 44

h + x = 22

Therefore, the number of students studying H = h + x + 20 + 10 = 22 + 20 + 10 = 52.

Let the number of students who studying only H be h, only E be e, only H and P but not E be x, only E and P but not H be y

Given only P = 0 All three = 10; Studying only H and E but not P = 20

Given number of students studying H = Number of students studying E

= h + x + 20 + 10

= e + y + 20 + 10

h + x = e + y total number of students = 74

Therefore, h + x + 20 + 10 + e + y = 74

h + x + e + y = 44

h + x + h + x = 44

h + x = 22

Therefore, the number of students studying H = h + x + 20 + 10 = 22 + 20 + 10 = 52.

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