d) The sum $\dots$ 9779 Ans: $\text{Digits} = 1, 2, 3, 5$ $L = 5{,}321$ $S = 1235$ $\text{Sum} = 6556 < 9779$ --- Q2. What is the $\dots$ difference? Ans: Smallest 5 digit palindrome $= 10001$ Large 5 digit palindrome $= 99999$ $\text{Sum} = 10001 + 99999 = 110000$ $\text{Difference} = 99999 - 10001 = 89998$ --- Q3. The time $\dots$ after that Ans: $\text{Time now} = 10:01$ $\text{Next Palindrome} = 11:11$ $\text{Difference} = 11:11 - 10:01 = 70 \text{ min} = 1 \text{ hour } 10 \text{ min}$ Next one is $12:21$ , after $2 \text{ hours } 10 \text{ min}$ . --- Q4. How many $\dots$ Ans: $\begin{array}{r r r} 8653 & 77 & 85 \\ - 3568 & - 13 & - 2\phantom{0} \\ \hline 5085 & 63 & 6\phantom{0} \end{array}$

Answer: Sum = 110000, Difference = 89998

Step-by-step solution

Step 1: Identify the smallest 5-digit palindrome

A $5$ -digit number has the form abcba, where the first digit $a$ cannot be $0$ . To minimize the number, we choose the smallest non-zero digit for $a$ , which is $1$ . To make the middle digits as small as possible, we choose $b = 0$ and $c = 0$ , giving $10001$ .

Step 2: Identify the largest 5-digit palindrome

To maximize a $5$ -digit number of the form abcba, each digit should be as large as possible. The largest single digit is $9$ , so setting $a = 9$ , $b = 9$ , and $c = 9$ gives the palindrome $99999$ .

Step 3: Calculate the sum

Adding the smallest $5$ -digit palindrome $10001$ to the largest $5$ -digit palindrome $99999$ gives $10001 + 99999 = 110000$ .

Step 4: Calculate the difference

Subtracting the smallest $5$ -digit palindrome $10001$ from the largest $5$ -digit palindrome $99999$ gives $99999 - 10001 = 89998$ .

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