CAT 2004 Question 6

Instructions

Directions for the following two questions: Answer the questions on the basis of the information given below.

In an examination, there are 100 questions divided into three groups A, B and C such that each group contains at least one question. Each question in group A carries 1 mark, each question in group B carries 2 marks and each question in group C carries 3 marks. It is known that the questions in group A together carry at least 60% of the total marks.

Question 6

If group B contains 23 questions, then how many questions are there in group C?

Solution

Group B contains 23 questions => Marks of group B = 46
Let the number of questions in A be x and in C be 77-x.
Marks of group A = x
So, x/(x+46+3*77-3x) >= 60%
=> 5x >= 3(277-2x)
=> 11x >= 831
=> x >= 75.54
=> x = 76 (min)
So, the possible number of questions in group C = 1.



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