If 1 is added to each odd digit and 2 is subtracted from each even digit in the number 8317456, what will be the sum of the digits that are second from the left and second from the right?
Understanding the Digit Modification Rules
The problem asks us to modify a given number, 8317456, based on specific rules for its digits. We need to add 1 to every odd digit and subtract 2 from every even digit. After modifying the digits, we need to find the sum of two specific digits: the one that is second from the left and the one that is second from the right in the modified number.
Applying Rules to Digits
Let's break down the original number 8317456 digit by digit and apply the given rules:
| Original Digit | Parity | Operation | Calculation | Modified Digit |
|---|---|---|---|---|
| 8 | Even | Subtract 2 | $8 - 2$ | 6 |
| 3 | Odd | Add 1 | $3 + 1$ | 4 |
| 1 | Odd | Add 1 | $1 + 1$ | 2 |
| 7 | Odd | Add 1 | $7 + 1$ | 8 |
| 4 | Even | Subtract 2 | $4 - 2$ | 2 |
| 5 | Odd | Add 1 | $5 + 1$ | 6 |
| 6 | Even | Subtract 2 | $6 - 2$ | 4 |
Forming the Modified Number
After applying the operations, the sequence of modified digits forms the new number. Combining the results from the table above, the modified number is 6428264.
Identifying Specific Digits
Now, we need to find the digits that are second from the left and second from the right in the modified number 6428264.
- The digits in 6428264 from left to right are: 6, 4, 2, 8, 2, 6, 4.
- The digit second from the left is the 2nd digit, which is 4.
- The digits in 6428264 from right to left are: 4, 6, 2, 8, 2, 4, 6.
- The digit second from the right is the 2nd digit from the end, which is 6.
Calculating the Final Sum
The final step is to sum the two identified digits:
- Second digit from the left: 4
- Second digit from the right: 6
- The sum is $4 + 6 = 10$.
Therefore, the sum of the digits that are second from the left and second from the right in the modified number is 10.
Important Questions from Number System
- The number 253118139 is divisible by which of the following?
- The number of prime numbers lying between 476 and 485, both included, is:
- The product of two consecutive natural numbers is 6. The greater of the two numbers is:
- Which of the following numbers divides 386937355?
This question is based on the five, three-digit numbers given below.
(Left) 126 257 352 984 751 (Right)
(Example- 697 - First digit = 6, second digit = 9 and third digit = 7)
(NOTE: All operations to be done from left to right.)
If 2 is added in the third digit of each number, how many numbers thus formed will be odd numbers?
