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Question:

Each question is followed by two statements A and B. Answer each question using the following instructions.
Mark (1) if the question can be answered by using statement A alone but not by using statement B alone.
Mark (2) if the question can be answered by using statement B alone but not by using statement A alone.
Mark (3) if the question can be answered by using both the statements together but not by using either of the statements alone.
Mark (4) if the question cannot be answered on the basis of the two statements.

The average weight of a class of 100 students is 45 kg. The class consists of two sections, I and II, each with 50 students. The average weight, W_I, of Section I is smaller than the average weight, W_II, of Section II. If the heaviest student, say Deepak, of Section II is moved to Section I, and the lightest student, say Poonam, of Section I is moved to Section II, then the average weights of the two sections are switched, i.e., the average weight of Section I becomes W_II and that of Section II becomes W_I. What is the weight of Poonam?

A. W_II – W_I = 1.0
B. Moving Deepak from Section II to I (without any move from I to II) makes the average weights of the two sections equal.

Explanation:

Let the weights of Deepak and Poonam be d and p respectively.

(50W_II + 50W_I)/100 = 45

∴ W_II + W_I = 90 ...(i)

50W_I + d – p = 50W_II

50W_II – d + p = 50W_I

∴ 50(W_II – W_I) = d – p ...(ii)

From Statement A, W_II – W_I = 1 ...(iii)

From (i), (ii) and (iii)

W_I and W_II can be found. Also, d – p = 50 ...(iv)

However this information does not give us the value of p. Statement A is insufficient to answer the question.

From Statement B,

W_I = W_II = (Sum_I + d)/51 = (Sum_II – d)/49

∴ 49(Sum_I) + 49d = 51(Sum_II) – 51d

∴ 100d = 51(50W_II) – 49(50W_I)

∴ 2d = 51W_II – 49W_I ...(v)

This alone cannot help us find the value of p. Statement B is insufficient to answer the question.

Considering both statements together, we have values of W_I and W_II, which can be substituted in (v) to find d, which can be used to find p using (iv).

Hence, option (c).

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