Refer to the following number series and answer the question that follows.…
2025
Refer to the following number series and answer the question that follows. Counting to be done from left to right only. (All numbers are single-digit numbers only.)
(Left) 8 5 6 4 1 2 4 5 7 5 9 6 3 2 1 5 8 4 5 6 7 5 (Right)
How many such even digits are there which are immediately preceded by an odd digit and also immediately followed by an even digit?
- A.
Two
- B.
Three
- C.
Four
- D.
One
Attempted by 3 students.
Show answer & explanation
Correct answer: B
Concept: A digit at some position qualifies only when the digit itself is even, the digit immediately to its left is odd, AND the digit immediately to its right is even — that is, three consecutive positions must show the pattern Odd → Even → Even, and only the middle digit of that triplet is counted. The very first and very last digits of the series can never qualify, because one side has no neighbour to check.
Application: The series, numbered left to right, is: 1-8, 2-5, 3-6, 4-4, 5-1, 6-2, 7-4, 8-5, 9-7, 10-5, 11-9, 12-6, 13-3, 14-2, 15-1, 16-5, 17-8, 18-4, 19-5, 20-6, 21-7, 22-5. Since only an even digit can be the target, check the neighbours of every even digit in the series:
Position | Previous digit | Digit (even) | Next digit | Pattern Odd→Even→Even? |
|---|---|---|---|---|
1 (first digit) | — (no left neighbour) | 8 | 5 | No — boundary position, cannot qualify |
3 | 5 (odd) | 6 | 4 (even) | Yes — qualifies |
4 | 6 (even) | 4 | 1 (odd) | No — previous digit is even |
6 | 1 (odd) | 2 | 4 (even) | Yes — qualifies |
7 | 2 (even) | 4 | 5 (odd) | No — previous even, next odd |
12 | 9 (odd) | 6 | 3 (odd) | No — next digit is odd |
14 | 3 (odd) | 2 | 1 (odd) | No — next digit is odd |
17 | 5 (odd) | 8 | 4 (even) | Yes — qualifies |
18 | 8 (even) | 4 | 5 (odd) | No — previous even, next odd |
20 | 5 (odd) | 6 | 7 (odd) | No — next digit is odd |
Cross-check: Re-verify each qualifying triplet directly against the raw series: (5, 6, 4) at positions 2-3-4 is Odd→Even→Even; (1, 2, 4) at positions 5-6-7 is Odd→Even→Even; (5, 8, 4) at positions 16-17-18 is Odd→Even→Even. No other even digit in the series has both neighbours matching this pattern, so the tally of three qualifying digits (at positions 3, 6 and 17) is confirmed.
Result: Three even digits — the ones at positions 3, 6 and 17 — are each immediately preceded by an odd digit and immediately followed by an even digit.