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Question

If 1 is added to each odd digit and 2 is subtracted from each even digit in the number 8574162, what will be the sum of the digits which are second from the left and second from the right in the new number thus formed?

The correct answer is

10

The problem asks us to modify the digits of a given number based on whether they are odd or even, and then find the sum of two specific digits in the resulting number.

Step 1: Understand the Transformation Rules

The rules for transforming the digits of the number 8574162 are:

  • If a digit is odd, add 1 to it.
  • If a digit is even, subtract 2 from it.

Step 2: Apply the Rules to Each Digit

Let's process each digit of the number 8574162:

  • 8 (Even): $8 - 2 = 6$
  • 5 (Odd): $5 + 1 = 6$
  • 7 (Odd): $7 + 1 = 8$
  • 4 (Even): $4 - 2 = 2$
  • 1 (Odd): $1 + 1 = 2$
  • 6 (Even): $6 - 2 = 4$
  • 2 (Even): $2 - 2 = 0$

Step 3: Form the New Number

After applying the transformations, the sequence of digits becomes 6, 6, 8, 2, 2, 4, 0. So, the new number formed is 6682240.

Step 4: Identify the Required Digits

We need to find the digits that are:

  • Second from the left: In the number 6682240, the digits from left to right are 6, 6, 8, 2, 2, 4, 0. The second digit from the left is 6.
  • Second from the right: The digits from right to left are 0, 4, 2, 2, 8, 6, 6. The second digit from the right is 4.

Step 5: Calculate the Sum

The final step is to calculate the sum of the two identified digits:

Sum = (Digit second from the left) + (Digit second from the right)

Sum = $6 + 4$

Sum = $10$

Therefore, the sum of the digits which are second from the left and second from the right in the new number is 10.

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