 All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars  perplexus dot info  Three problems (Posted on 2004-01-16) In a contest of intelligence, three problems A, B and C were posed.

Among the contestants there were 25 who solved at least one problem each.

Of all the contestants who did not solve problem A, the number who solved B was twice the number who solved C.

The number of participants who solved only problem A was one more than the number who solved problem A and at least one other problem.

Of all students who solved just one problem, half did not solve problem A.

How many students solved only problem B?

 Submitted by Ravi Raja Rating: 3.6000 (5 votes) Solution: (Hide) 6 students solved only problem B X => Students who solved only problem A Y => Students who solved only problem B Z => Students who solved only problem C P => Students who solved both problem B and problem C From 4 : Students who solved only problem A = Students who solved only problem B + Students who solved only problem C X = Y + Z From 3 : Students who solved problem A and at least one other = X - 1 From 2 : (Y + P) = 2 * (Z + P) Y + P = 2 * Z + 2 * P Z = (Y - P) / 2 From 1: X + X - 1 + Y + Z + P = 25 2*X + Y + Z + P = 26 2*(Y + Z) + Y + Z + P = 26 (from 4) 3*Y + 3*Z + P = 26 3*Y + 3* (Y - P) / 2 + P = 26 (from 2) 6*Y + 3*Y - 3*P + 2*P = 52 9*Y - P = 52 Y = (52 + P) / 9 Now, it is obvious that all values are integer. Hence, P must be 2 and Y must be 6. So 6 students solved only problem B. Subject Author Date answer K Sengupta 2007-12-23 12:07:24 solution SilverKnight 2004-01-16 10:51:05 solution Charlie 2004-01-16 10:34:12 Please log in:

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