20) Six weights of 2, 3, 5, 7, 9, 10 hectograms are available. Five of them are placed on the two plates of a balance in such a way that it is in equilibrium. Which weight is excluded?
(A) 2 (B)
(C) 5
(D) 10
(E) cannot be determined.
20) The answer is (A). The sum of all weights is 36 hectograms. If the balance is to be in equilibrium, the sum of the 5 chosen weights must be even, so only an even weight can be removed. Excluding the 10 hectogram weight, 13 hectograms should be placed on each plate, and this cannot be achieved with the 5 remaining weights. Excluding instead the 2 hectogram weight, 17 hectograms should be placed on each plate, which can be achieved by placing 3, 5, and 9 hectograms on one plate and 7 and 10 hectograms on the other.