Question

Question: What is the total weight of 12 metal discs having equal weight?
Statements:
I. Half of the weight of a metal disc is 8 kg.
II. The total weight of 4 discs is 32 kg more than the total weight of two discs.

• A. Statement I is sufficient but statement II is not sufficient
• B. Statement II is sufficient but statement I is not sufficient
• C. Either statements I or II is sufficient
• D. Both the statements together are not sufficient

Hint:

In data sufficiency, test each statement independently.

Answer 1

The Correct Option is C

To determine the total weight of 12 metal discs, we need to assess the information provided in the statements individually:

1. Statement I: Half of the weight of a metal disc is 8 kg.

If half of the weight of a metal disc is 8 kg, then the full weight of one metal disc is \(2 \times 8 = 16\) kg.

The total weight of 12 metal discs would therefore be \(12 \times 16 = 192\) kg. Hence, statement I is sufficient on its own.

1. Statement II: The total weight of 4 discs is 32 kg more than the total weight of two discs.

Let's denote the weight of one metal disc as \(x\) kg.

Based on the information given:

\(4x = 2x + 32\)

Simplifying the equation:

\(4x - 2x = 32\)

\(2x = 32\)

\(x = 16\)

Therefore, the weight of one disc is also found to be 16 kg using statement II. Thus, the total weight of 12 discs is \(12 \times 16 = 192\) kg. This means statement II is also sufficient on its own.

Since either statement I or II alone allows us to determine the total weight of the 12 metal discs, the correct answer is Either statements I or II is sufficient.