CAT 2007 Question 1

Instructions

Directions for the following four questions: Each question is followed by two statements A and B. Indicate your responses based on data sufficiency

Question 1

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.

Solution

Let w1 and w2 be average of both the groups respectively.

Since average of whole class is 45. $$\frac{50*w1+50*w2}{100} = 45 $$ => w1 + w2 = 90

And if we consider case A we have w2-w1 = 1. From the two equations average weight can be found out.

Further using the equations deduced from given condition which are : $$\frac{50*w1-l+h}{50} = w2$$ and $$\frac{50*w2+l-h}{50} = w1$$ where l and h is weight of poonam and deepak respectively. However, both of the above equations are effectively the same. Hence we have two equations and 3 unknowns, thus we cannot find the weights by using statement I alone.

If we consider statement B, then we can get another equation. So we will have 3 equations and then we can solve them for the 3 variables.
So both the equations are required to answer the question.



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