Directions: Each item in this section contains a question followed by two statements. Answer each item using the following instructions:
(a) Select this option if the question can be answered using one of these statements alone, but cannot be answered using other statement
(b) Select this option if the question can be answered using either statement alone
(c) Select this option if the question can be answered using both the statements together, but cannot be answered using either statement alone
(d) Select this option if the question cannot be answered even using any of the statements
Question: X receives three coins of different denominations : 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.
A.(a)✓ Correct
B.(b)
C.(c)
D.(d)
Explanation
We need to determine if X received a coin of denomination 5, given three coins from {1, 2, 5, 10, 20}. Statement II alone: if sum of digits of m > 5, we test combinations. The possible sums without a 5-coin from {1,2,10,20}: 1+2+10=13 (digit sum 4), 1+2+20=23 (5), 1+10+20=31 (4), 2+10+20=32 (5). None give digit sum > 5. With a 5-coin: 1+2+5=8 (8), 1+5+10=16 (7), 1+5+20=26 (8), 2+5+10=17 (8), 2+5+20=27 (9), 5+10+20=35 (8). All combinations with 5 give digit sum > 5. So Statement II alone determines yes. Statement I alone: m not prime—many composite values exist both with and without 5 (e.g., 32 without 5; 8 with 5), so insufficient. Hence only Statement II answers it.
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