Directions: The next three items are based on a survey on 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 If “O” and “U”, irrespective of upper or lower case, occur exactly 5040 times, then how many times does the letter “E” occur in the book in the upper or the lower case?

Correct — D, 11340. Percentages become counts as soon as one per cent is priced. From the shared table, O is 8% and U is 12%, so together they are 20% of all the vowel occurrences counted. That 20% is given as 5,040 occurrences, so 1% corresponds to 5,040 ÷ 20 = 252 occurrences. E is 45%, so E occurs 45 × 252 = 11,340 times. The whole survey covers 100 × 252 = 25,200 vowel occurrences, and 45% of 25,200 is 11,340 — the same answer reached the other way round, which is a quick way to check it.

• (a)11840 — 500 too many. It does not correspond to any whole percentage of a consistent total — 11,840 ÷ 252 is not a whole number of percentage points.
• (b)11600 — Close to the true value but again not a multiple of 252, so it cannot be any whole percentage of the same book.
• (c)11430 — The nearest decoy, differing from the answer only by a transposition of the last two digits. It is a warning to write the multiplication out rather than eyeball the options.

A percentage table has no absolute scale until one figure is pinned to a real count. Pin any one of them and the entire table becomes a table of counts, because all the entries share the same base. Here the pinning is done indirectly, through the combined figure for two vowels rather than a single one, which is the only wrinkle in the question.

The reliable method is to reduce everything to what one per cent is worth. O + U = 8 + 12 = 20% and that equals 5,040, so one per cent is 252. From there every other entry follows in one multiplication: A is 20% or 5,040 — the same as O and U together, which is a neat internal check — E is 45% or 11,340, and I is 15% or 3,780. The total is 25,200. The error to avoid is dividing 5,040 by 8 or by 12, treating the given count as belonging to one vowel rather than to the two together; that path gives 630 or 420 per percentage point and lands nowhere near an option. It is also worth noticing that the answer is exactly 2¼ times the given 5,040, since 45 is 2¼ times 20 — a candidate who spots that ratio can finish the item in a single step.

• The shared data set: A 20%, E 45%, I 15%, O 8%, U 12%.
• O + U = 20% of all letters counted, and that equals 5,040 occurrences.
• One per cent therefore equals 5,040 ÷ 20 = 252 occurrences.
• E is 45%, so E occurs 45 × 252 = 11,340 times.
• The whole survey covers 100 × 252 = 25,200 vowel occurrences; A occurs 5,040 times, I 3,780.

• Dividing 5,040 by 8 or by 12 instead of by the combined 20.
• Reading the answer off a near-neighbour option such as 11,430 without completing the multiplication.
• Forgetting that the given count covers two vowels together, not one.

Asked as the closing item of a three-question data set, where a single absolute figure is supplied and everything else must be scaled from it.

• practice — not a real PYQ

  In the same survey, if O and U together occur 5040 times, how many times does the vowel A occur?

  • (a)3780
  • (b)5040
  • (c)6300
  • (d)11340

  Answer(b) 5040 — one per cent is 252, and A is 20%, so A occurs 20 × 252 = 5,040 times, coincidentally the same as O and U together.

• practice — not a real PYQ

  In the same survey, if O and U together occur 5040 times, what is the total number of vowel occurrences counted?

  • (a)20160
  • (b)25200
  • (c)27720
  • (d)30240

  Answer(b) 25200 — one per cent is 252, so the whole hundred per cent is 100 × 252 = 25,200.