Question

Refer to the following series and answer the question (all numbers are single digit numbers only).

(Left) 6 2 1 3 7 6 9 7 4 3 5 2 3 4 3 4 2 3 1 5 7 9 5 8 5 7 5 (Right)

How many such even digits are there each of which is immediately preceded by an even digit and also immediately followed by an odd digit?

• A. 1
• B. 2
• C. 3
• D. 0

Answer 1

Answer:

B. 2

We are looking for a specific three-digit pattern: Even — Even — Odd.

• The middle digit must be Even.

• The preceding (left) digit must be Even.

• The following (right) digit must be Odd.

Let's look at all the even digits in the series (excluding the very first one, since it has no preceding digit) and check their neighbors:

1. 6 2 1 3...

   • Look at 2: Preceded by 6 (Even), Followed by 1 (Odd).

   • Match found(6, 2, 1)

2. ...1 3 7 6 9...

   • Look at 6: Preceded by 7 (Odd).

   • No match.

3. ...9 7 4 3...

   • Look at 4: Preceded by 7 (Odd).

   • No match.

4. ...3 5 2 3...

   • Look at 2: Preceded by 5 (Odd).

   • No match.

5. ...2 3 4 3...

   • Look at 4: Preceded by 3 (Odd).

   • No match.

6. ...3 4 3 4 2...

   • Look at the next 4: Preceded by 3 (Odd).

   • No match.

7. ...4 3 4 2 3...

   • Look at 2: Preceded by 4 (Even), Followed by 3 (Odd).

   • Match found(4, 2, 3)

8. ...2 3 1 5 7 9 5 8 5...

   • Look at 8: Preceded by 5 (Odd).

   • No match.

Conclusion

There are exactly 2 such even digits in the series.

They appear in the following combinations:

• 6, 2, 1 (The digit 2)

• 4, 2, 3 (The digit 2)