CAPF AC 2023 Q78: General Mental Ability – Data Interpretation
- (a) 4
- (b) 5
- (c) 6
- (d) 7
Answer: (b) 5
Explanation
Pairs of vowels above 34%
How to think: the chance of any one of the two is the sum of their percentages.
Five vowels give 10 pairs.
List all ten and count those above 34.
Data: the survey gives the percentage occurrence of each vowel in a certain book, irrespective of whether it is in upper or lower case.
A = 20, E = 45, I = 15, O = 8, U = 12.
| Pair | Sum | More than 34%? |
|---|---|---|
| A, E | 65 | Yes |
| A, I | 35 | Yes |
| A, O | 28 | No |
| A, U | 32 | No |
| E, I | 60 | Yes |
| E, O | 53 | Yes |
| E, U | 57 | Yes |
| I, O | 23 | No |
| I, U | 27 | No |
| O, U | 20 | No |
Faster way: E alone is 45, so every pair with E passes.
That gives 4 pairs.
Without E, only A + I = 35 passes.
Total = 4 + 1 = 5.
Answer: (b) 5.
Why each option is right or wrong
- (a) Incorrect. 4 counts only the pairs with E and misses the pair A and I (35%).
- (b) CORRECT. Four pairs with E, plus A and I, give 5 pairs above 34%.
- (c) Incorrect. 6 would need A and U to pass, but 20 + 12 is only 32.
- (d) Incorrect. 7 wrongly counts A and U (32%) and I and U (27%).
Key point
Any one of two = add the percentages. E (45) passes with every vowel: 4 pairs. Only A + I (35) passes without E. Total 5.
Remember
Either of two = add. Pairs above 34%: four with E, plus A and I.
Common mistakes
- Counting A and U (32%) as more than 34%.
- Forgetting the pair A and I, which just crosses the line at 35%.
- Multiplying the two percentages instead of adding them.
Exam tip
Start with the biggest value. If it alone crosses the limit, all its pairs pass; then test only the rest.
Sources
- NCERT Class X Mathematics — Probability
- Arun Sharma — How to Prepare for Data Interpretation for the CAT (Tata McGraw-Hill)