Question Details

How many such pairs of digits are there in the number ‘40585636’, each of which has as many digits between them as they have in the number series (Only in backward direction)?

Options

A

One

B

None

C

Two

D

More than three

Show Answer

Correct Answer :

Option C

Two

Two

Solution :

The correct answer is Two.

To find the number of digit pairs that satisfy the given condition, we look for pairs of digits in the number 40585636 that have the same number of digits between them as they do in the standard number series, but only in the backward (decreasing) direction.

First, let us write down the digits of the number along with their positions from left to right:
Digit: 4 (Pos 1), 0 (Pos 2), 5 (Pos 3), 8 (Pos 4), 5 (Pos 5), 6 (Pos 6), 3 (Pos 7), 6 (Pos 8)

Since we are only considering the backward direction (decreasing numerical order: 9, 8, 7, 6, 5, 4, 3, 2, 1, 0), we search for pairs where the digit at the higher position decreases step-by-step to match the digit at the lower position:

1. Checking from the digit 6 at Position 8:
Counting backward from 6:
• Position 7: 5 (Actual digit is 3)
• Position 6: 4 (Actual digit is 6)
• Position 5: 3 (Actual digit is 5)
• Position 4: 2 (Actual digit is 8)
• Position 3: 1 (Actual digit is 5)
• Position 2: 0 (Actual digit is 0) ⇒ Match!
Thus, the pair (6, 0) at positions 8 and 2 is a valid pair in the backward direction.

2. Checking from the digit 6 at Position 6:
Counting backward from 6:
• Position 5: 5 (Actual digit is 5) ⇒ Match!
Thus, the pair (6, 5) at positions 6 and 5 is a valid pair in the backward direction.

There are no other pairs that satisfy the backward decreasing numerical count. Therefore, there are exactly two such pairs.

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