MGmat wrong answer in Practice test

[satishchandra.aily]

In a group of 68 students, each student is registered for at least one of three classes - History, Math and English. Twenty-five students are registered for History, twenty-five students are registered for Math, and thirty-four students are registered for English. If only three students are registered for all three classes, how many students are registered for exactly two classes?
A)13 B)10 C)9 D)8 E)7

Mgmat has wrongly given the answer as 10.

Its a simple problem. My method of solving is as follows. Instead of suggesting a different method of solving the problem, find out the flaw in my method.
H-History, M-Math, E-English; Not Mutually exclusive



(H U M U E) = H + M + E - H^M - M^E - E^H + H^M^E

68 = 25+25+24-(H^M + M^E + E^H) + 3

(H^M + M^E + E^H) = 9

My answer is 9.

[rocsid.g91]

Ummm actually there's a flaw in your reasoning and your substitution.
(H U M U E) = H + M + E - H^M - M^E - E^H + H^M^E

Man this formula after tons of practice still makes no sense to me, so i don't use it. :-)
Either ways you've substituted 24 for 34. So that's an error.

This is the reasoning I used.
68 people out of which 3 members are in all three = 65 ( 1 class plus 2 classes)
25 members out of which 3 members are in all three = 22 ( 1 class plus 2 classes)
25 members out of which 3 members are in all three = 22 ( 1 class plus 2 classes)
34 members out of which 3 members are in all three = 31 ( 1 class plus 2 classes)

22 + 22 + 31 = 75 ( 1 class plus 2 classes)
75-65 = 10.

I believe manhattan's right.

[jnelson0612]

Thank you rocsid. The answer is indeed 10. This thread may shed more light on it: overlapping-sets-t1960.html