CAT 1996 | Question: 182

Question

In each question, you are given certain data followed by two statements. For answering the questions:

Mark a, if both the statements together are insufficient to answer the question.

Mark b, if any one of the two statements is sufficient to answer the question.

Mark c, if each statement alone is sufficient to answer the question.

Mark d, if both the statements together are sufficient to answer the question, but neither statement alone is sufficient.

What is the number of type 2 widgets produced, if the total number of widgets produced is $20,000$?

1. If the production of type- 1 widgets increases by $10$% and that of type-2 decreases by $6$%, the total production remains the same.

2. The ratio in which type- 1 and type- 2 widgets are produced is $2: 1$.

Answer 1

From the main statement , we have total  number of widgets is 20,000.

From 1st statement, we get
1.1 type-1 + 0.94 type-2 = 20,000.                              -------------- (i)

From this only we can't deduce, the required value.

From 2nd statement, we get,  type-1 = 2 type-2.        --------------(ii)

Putting this in (i), we can get values of both the widgets.

Hence, both the statements are required.

Option D is correct.