Data Sufficiency - Weight of a student after swapping

CAT 2007 Slot 1 · QA · Medium · Data Sufficiency

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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, WIW_I, of Section I is smaller than the average weight WIIW_{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 WIIW_{II} and that of Section II becomes WIW_I. What is the weight of Poonam?

A: WII−WI=1.0W_{II} - W_I = 1.0. B: Moving Deepak from Section II to I (without any move I to II) makes the average weights of the two sections equal.

  1. A.

    Question can be answered using A alone but not using B alone

  2. B.

    Question can be answered using B alone but not using A alone

  3. C.

    Question can be answered using A and B together, but not using either A or B alone

  4. D.

    Question cannot be answered even using A and B together

Answer

C

Explanation

Let Deepak's weight be DD and Poonam's weight be PP. Using A: gives WII−WI=1.0W_{II} - W_I = 1.0. Using B: allows us to express DD in terms of section averages. Combining both statements gives enough information to solve for PP.

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