CAPF AC 2020 Q123: General Mental Ability – Logical Reasoning & Puzzles
What is the value of the missing number?
- (a) 9
- (b) 7
- (c) 5
- (d) 3
Answer: (a) 9
Explanation
Missing number in the circle
How to think: each sector has a pair outside and one number inside.
First try the simplest link: add the pair.
The sum does not match the number in its own sector, so look at the sector directly opposite.
Rule: sum of the outer pair = inner number of the opposite sector.
| Sector | Outer pair | Sum | Inner number of the opposite sector |
|---|---|---|---|
| 1 | (3, 4) | 7 | 7 |
| 2 | (1, 5) | 6 | 6 |
| 3 | (3, 2) | 5 | 5 |
| 4 | (3, 1) | 4 | 4 |
| 5 | (2, 3) | 5 | 5 |
| 6 | (2, 7) | 9 | ? |
| 7 | (1, 2) | 3 | 3 |
| 8 | (2, 6) | 8 | 8 |
The missing number sits opposite the pair (2, 7).
So the missing number is 2 + 7 = 9.
Answer: (a) 9.
Why each option is right or wrong
- (a) CORRECT. The opposite pair is (2, 7), and 2 + 7 gives the missing number 9.
- (b) Incorrect. 7 is only one member of the opposite pair, not the sum of the pair.
- (c) Incorrect. 5 is the difference of 7 and 2; the rule uses the sum.
- (d) Incorrect. 3 is the sum of the pair (1, 2), which belongs to a different sector.
Key point
Circle puzzle rule: add the outer pair; the sum is the inner number of the opposite sector. (2, 7) gives 9.
Remember
Outer pair sum = inner number opposite: 2 + 7 = 9.
Common mistakes
- Adding the pair (1, 5) in the same sector as the question mark and looking for 6.
- Trying multiplication or difference before testing the simple sum.
- Not checking the rule on at least two other sectors before marking the answer.
Exam tip
In circle puzzles test three links in order: same sector, next sector, opposite sector.
Sources
- R. S. Aggarwal — A Modern Approach to Verbal and Non-Verbal Reasoning (inserting the missing character)
- Arun Sharma — How to Prepare for Logical Reasoning for the CAT (series and missing-number puzzles)