Question

In the series given below how many 8s are there each of which is exactly divisible by its preceding as well as succeeding numbers?
2, 8, 3, 8, 2, 4, 8, 2, 4, 8, 6, 8, 2, 8, 2, 4, 8, 3, 8, 2, 8, 6

• A. 1
• B. 2
• C. 3
• D. 4

Hint:

Since the number is 8, its only single-digit divisors are 1, 2, 4, and 8. Therefore, any 8 surrounded by numbers containing 3, 5, 6, 7, or 9 can be instantly crossed out without performing any division.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
We need to find the number of times the digit '8' appears in the given sequence such that 8 is completely divisible (leaving a remainder of 0) by both the number immediately before it (preceding) and the number immediately after it (succeeding).

Step 2: Detailed Explanation:
Let us identify all the occurrences of 8 and check their preceding and succeeding numbers:
1. First 8: \( 2, \mathbf{8}, 3 \)
- Preceding: 2 (8 is divisible by 2)
- Succeeding: 3 (8 is not divisible by 3) \(\rightarrow\)

No
2. Second 8: \( 3, \mathbf{8}, 2 \)
- Preceding: 3 (8 is not divisible by 3) \(\rightarrow\)

No
3. Third 8: \( 4, \mathbf{8}, 2 \)
- Preceding: 4 (8 is divisible by 4)
- Succeeding: 2 (8 is divisible by 2) \(\rightarrow\)

Yes (1)
4. Fourth 8: \( 4, \mathbf{8}, 6 \)
- Preceding: 4 (8 is divisible by 4)
- Succeeding: 6 (8 is not divisible by 6) \(\rightarrow\)

No
5. Fifth 8: \( 6, \mathbf{8}, 2 \)
- Preceding: 6 (8 is not divisible by 6) \(\rightarrow\)

No
6. Sixth 8: \( 2, \mathbf{8}, 2 \)
- Preceding: 2 (8 is divisible by 2)
- Succeeding: 2 (8 is divisible by 2) \(\rightarrow\)

Yes (2)
7. Seventh 8: \( 4, \mathbf{8}, 3 \)
- Preceding: 4 (8 is divisible by 4)
- Succeeding: 3 (8 is not divisible by 3) \(\rightarrow\)

No
8. Eighth 8: \( 3, \mathbf{8}, 2 \)
- Preceding: 3 (8 is not divisible by 3) \(\rightarrow\)

No
9. Ninth 8: \( 2, \mathbf{8}, 6 \)
- Preceding: 2 (8 is divisible by 2)
- Succeeding: 6 (8 is not divisible by 6) \(\rightarrow\)

No
Thus, there are exactly 2 such 8s in the series (in the triplets \( 4, \mathbf{8}, 2 \) and \( 2, \mathbf{8}, 2 \)).

Step 3: Final Answer:
(B) 2