CAPF AC 2022 Q34: General Mental Ability – Quantitative Aptitude
If the average of the first four of five numbers in decreasing order is 25 and the average of the last four numbers is 20, then what is the difference between the first and the last number?
- (a) 5
- (b) 10
- (c) 15
- (d) 20
Answer: (d) 20
Explanation
Difference between the first and last of five numbers
Given: five numbers are in decreasing order; the average of the first four is 25 and the average of the last four is 20; find the difference between the first and the last number.
How to think: the two groups share the middle three numbers.
Subtract the two sums and the shared numbers cancel out.
| Step | Working |
|---|---|
| Numbers | a, b, c, d, e |
| Sum of the first four | a + b + c + d = 25 × 4 = 100 |
| Sum of the last four | b + c + d + e = 20 × 4 = 80 |
| Subtract | a − e = 100 − 80 = 20 |
Answer: (d) 20.
Why each option is right or wrong
- (a) Incorrect. 5 is only the difference of the two averages, not of the numbers.
- (b) Incorrect. 10 has no basis; the sums differ by 20.
- (c) Incorrect. 15 has no basis; the sums are 100 and 80.
- (d) CORRECT. The sums are 100 and 80, so the first minus the last is 20.
Key point
Overlapping groups: convert averages to sums and subtract; common items cancel. Difference = (difference of averages) × (number of items in each group) = 5 × 4 = 20.
Remember
Difference of sums: 100 − 80 = 20.
Common mistakes
- Answering 5, the difference of the averages, without multiplying by 4.
- Trying to find all five numbers, which is neither possible nor needed.
- Dividing the difference of the sums by 4 again at the end.
Exam tip
Educated guess: the difference of the averages is 5 and each group has 4 numbers. 5 × 4 = 20.
Sources
- NCERT Class VII Mathematics — Data Handling (arithmetic mean)
- R. S. Aggarwal, Quantitative Aptitude — Average