Question

What is the number of type-2 widgets produced, if the total number of widgets produced is 20,000? The company produces only two types of widgets.

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.

• A. if the question cannot be answered even with the help of both the statements taken together.
• B. 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).
• C. if the question can be answered by any one of the two statements.
• D. if both statements I and II together are needed to answer the question.

Hint:

Let type-1 be x and type-2 be y with x + y = 20,000. Translate each statement into a second equation or ratio and see whether it alone fixes y.

Answer 1

The Correct Option is C

Step 1: Set up:
Let type-1 = x and type-2 = y, with x + y = 20,000.

Step 2: Statement I alone:
The new total is 1.10x + 0.94y, which equals the old total: 1.10x + 0.94y = x + y, so 0.10x = 0.06y and x : y = 3 : 5. Then y = (5/8) × 20,000 = 12,500. Sufficient.

Step 3: Statement II alone:
x : y = 2 : 1 gives y = (1/3) × 20,000 = 6,666.67 (about 6,667). Also a single value, so sufficient.

Step 4: Decide:
Each statement alone gives a definite answer to the question, so the question can be answered by any one of the two statements.

Final Answer:
The correct option is (3): the question can be answered by any one of the two statements.