CAPF AC 2023 Q79: General Mental Ability – Data Interpretation
The next three items are based on a survey on the occurrence of vowels in a certain book, irrespective of whether they are in upper or lower case:
| Vowel | A | E | I | O | U |
|---|---|---|---|---|---|
| Percentage | 20 | 45 | 15 | 8 | 12 |
Among the three vowels which occur minimum number of times, what is the percentage of occurrence of the letter that occurs the maximum number of times among them?
- (a) 42 6/7 %
- (b) 41 5/7 %
- (c) 40 4/7 %
- (d) 39 2/7 %
Answer: (a) 42 6/7 %
Explanation
Share of the largest among the three least common vowels
How to think: do it in three steps.
Pick the three smallest values, find their total, then take the largest of the three as a share of that total.
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.
| Step | Working |
|---|---|
| Three smallest | O = 8, U = 12, I = 15 |
| Their total | 8 + 12 + 15 = 35 |
| Largest of the three | I = 15 |
| Share of I | 15 / 35 = 3 / 7 |
| As a percentage | 300 / 7 = 42 6/7 % |
Check on the fraction:
| Fraction | Percentage |
|---|---|
| 1 / 7 | 14 2/7 % |
| 2 / 7 | 28 4/7 % |
| 3 / 7 | 42 6/7 % |
Answer: (a) 42 6/7 %.
Why each option is right or wrong
- (a) CORRECT. I is 15 out of 35, which is 3/7 or 42 6/7 %.
- (b) Incorrect. 41 5/7 % does not equal 15 out of 35; 300 divided by 7 leaves remainder 6.
- (c) Incorrect. 40 4/7 % is too low; 3/7 is 42 6/7 %.
- (d) Incorrect. 39 2/7 % is too low and has the wrong remainder.
Key point
Three least common vowels: O (8), U (12), I (15); total 35. Share of I = 15/35 = 3/7 = 42 6/7 %.
Remember
15 out of 35 = 3/7 = 42 6/7 %.
Common mistakes
- Taking I as a share of the whole book (15%) instead of the three vowels.
- Picking A as one of the three smallest; the smallest are O, U and I.
- Slipping on the division: 300 / 7 is 42 remainder 6.
Exam tip
Learn the sevenths: 1/7 is about 14.3%, so 3/7 is about 42.9%. Only one option is near it.
Sources
- NCERT Class VIII Mathematics — Comparing Quantities (percentages)
- Arun Sharma — How to Prepare for Data Interpretation for the CAT (Tata McGraw-Hill)