CAPF AC 2025 Q68: General Mental Ability – Logical Reasoning & Puzzles
- (a) 3
- (b) 2
- (c) 0
- (d) 1
Answer: (b) 2
Explanation
Four bulbs and complete darkness
Given: A is on 2 min and off 1 min; B on 3 and off 1; C on 4 and off 1; D on 5 and off 1. The man stays for one hour.
How to think: the cycle lengths are 3, 4, 5 and 6 minutes, and every bulb is off in the last minute of its own cycle.
All four are off together only in a minute that is the last minute of all four cycles.
| Bulb | Cycle | Off during minute numbers (counting from 0) |
|---|---|---|
| A | 3 min | 2, 5, 8, … (≡ 2 mod 3) |
| B | 4 min | 3, 7, 11, … (≡ 3 mod 4) |
| C | 5 min | 4, 9, 14, … (≡ 4 mod 5) |
| D | 6 min | 5, 11, 17, … (≡ 5 mod 6) |
Each number is one less than the cycle, so the minute must be one less than a common multiple. LCM(3, 4, 5, 6) = 60.
So the room is completely dark only in minute 59, 119, 179, … (the last minute of each hour of the cycle).
A one-hour stay must overlap one such minute. If the man enters in the middle of a dark minute (59.5) and leaves in the middle of the next one (119.5), he meets darkness at the start and at the end: 2 times. This is the maximum.
Bank key corrected: the stored key was (c) 0; the right answer is (b) 2.
Answer: (b) 2.
Why each option is right or wrong
- (a) Incorrect. A dark minute comes once every 60 minutes, so 3 is not possible in an hour.
- (b) CORRECT. Entering and leaving in the middle of dark minutes gives 2 meetings with darkness.
- (c) Incorrect. An hour-long stay must overlap at least one dark minute, so 0 is impossible.
- (d) Incorrect. 1 is the minimum, not the maximum, because he can meet two dark minutes at the two ends.
Key point
Cycles 3, 4, 5, 6 minutes; each bulb is off in the last minute of its cycle. All off together in minute 59 (mod 60). A 60-minute stay can cover parts of two dark minutes: maximum 2, minimum 1.
Remember
All four are off only in the last minute of each 60: the longest stay catches it at both ends.
Common mistakes
- Concluding that darkness never happens because the bulbs have different cycles.
- Stopping at 1 without noticing that the question asks for the maximum.
- Counting the bulbs' off times from 1 instead of from 0.
Exam tip
Educated guess: the word 'maximum' hints that the count is not fixed, which only happens if the stay can catch two dark minutes at its two ends. So choose 2.
Sources
- NCERT Class VI Mathematics, Chapter 3 (Playing with Numbers: LCM)
- R. S. Aggarwal, A Modern Approach to Verbal and Non-Verbal Reasoning, chapter on Puzzles