X receives three coins of different denominations from among 1, 2, 5, 10 and 20. If the total amount received by X is m, does X r…

Question

Directions: The question is followed by two statements. Answer using the codes given in the options.

X receives three coins of different denominations from among 1, 2, 5, 10 and 20. If the total amount received by X is m, does X receive a coin of denomination 5?

Statement I: m is not a prime number.

Statement II: The sum of the digits of m is greater than 5.

1. A. The question can be answered using one of the statements alone, but cannot be answered using the other statement alone. (Correct answer)
2. B. The question can be answered using either statement alone.
3. C. The question can be answered using both the statements together, but cannot be answered using either statement alone.
4. D. The question cannot be answered even using both the statements together.

Correct Answer

Option A — The question can be answered using one of the statements alone, but cannot be answered using the other statement alone.

Detailed Solution & Explanation

The correct answer is Option A (one statement alone suffices, the other does not).

Key Points

• Any 3 distinct denominations from {1, 2, 5, 10, 20} give sums: 8, 13, 16, 17, 23, 26, 27, 31, 32, 35.
• Statement II (digit-sum of m > 5) alone is sufficient: the qualifying totals are 8, 16, 17, 26, 27, 35 — and *every one of these combinations contains a 5-coin*, so the answer is definitely "Yes".
• Statement I (m not prime) alone is insufficient: m = 32 (= 2+10+20) is non-prime but has no 5-coin, while m = 8 (= 1+2+5) is non-prime and does contain a 5.

Additional Information

• Since exactly one statement settles the question and the other does not, the answer is Option A.