CAT 1996 — QA Question 46
Answer the questions based on the following information.
A series S1 of five positive integers is such that the third term is half the first term and the fifth term is 20 more than the first term. In series S2, the nth term defined as the difference between the (n + 1)th term and the nth term of series S1, is an arithmetic progression with a common difference of 30.
Direction: Each question is followed by two statements, I and II. Mark the answer as
1. if the question cannot be answered even with the help of both the statements taken together.
2. if the question can be answered by any one of the two statements.
3. if each statement alone is sufficient to answer the question, but not the other one (e.g. statement I alone is required to answer the question, but not statement II and vice versa).
4. if both statements I and II together are needed to answer the question.
What is the number of type-2 widgets produced, if the total number of widgets produced is 20,000?
I. If the production of type-1 widgets increases by 10% and that of type-2 decreases by 6%, the total production remains the same.
II. The ratio in which type-1 and type-2 widgets are produced is 2 : 1.
Answer & solution
Answer: 2
Consider the statement I:
Let number of type-1 widgets = x.
Number of type-2 widgets = y.
From the given question, x + y = 20000.
From statement I, 1.1 x + 0.94y = 20000.
So we can get x and y.
From statement II, number of type-2 widgets produced
× 20000 = 6667.
The question can be answered by using either of the statements alone.