$X$ 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 $5$.

Question

Accepted Answer

Select this option if the question can be answered using one of these statements alone, but cannot be answered using other statement

Explanation: List all possible combinations of three different coins: 1+2+5=8, 1+2+10=13, 1+2+20=23, 1+5+10=16, 1+5+20=26, 1+10+20=31, 2+5+10=17, 2+5+20=27, 2+10+20=32, 5+10+20=35. Statement I: Non-prime values are 8, 16, 26, 27, 32, 35—includes 32 (2+10+20) which lacks denomination 5, so insufficient. Statement II: Values with digit sum >5 are 8, 16, 17, 26, 27, 35—all include denomination 5, so sufficient. Therefore, Statement II alone answers the question but Statement I does not, making Option 1 the correct answer.

Detailed Explanation:

Question 2 of 2 Numerical Problems

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