In this guide
A caselet is a DI set with the table taken away. Instead of rows and columns, you get a paragraph: "Science has twice as many students as Arts", "sales rose by a quarter", "at least one of each was sold". The information is complete, but it is scattered through sentences, and some of it is hidden in words like "the rest" or "more than".
The skill is translation. Once the paragraph is a table, a caselet is an ordinary DI set. This guide shows how to design the table, how to turn each sentence into a cell or an equation, and how to handle the integer conditions that CAT uses to make a caselet's answer unique.
Why caselets feel hard
- The structure is not given. You decide the rows and columns, and a poor choice makes every question slower.
- Relationships, not values. "Twice as many", "60 more than", "20% higher" must each become an equation.
- Hidden conditions. "The rest", "each", "at least one", "more than" all carry information.
- Words that change the base. "20% higher than in April" and "20% of May's total" are different calculations.
The method
- Read the whole caselet once, without writing. Find the entities (people, products, months) and the attributes (units, revenue, share).
- Design the table. Entities as rows, attributes or time periods as columns, with a total row and column.
- Translate sentence by sentence. Each sentence becomes either a filled cell or an equation. Tick each sentence as you use it.
- Solve the equations, simplest first, and fill the table.
- Check every total and every sentence against the finished table before answering.
| Words in the caselet | Translation |
|---|---|
| "A is twice B" | A = 2B |
| "A is 60 more than B" | A = B + 60 |
| "A rose by 25%" | New A = 1.25 × old A |
| "A is 45% of the total" | A = 0.45 × total |
| "The rest were C" | C = total − (all others) |
| "At least one of each" | Every value ≥ 1 |
| "More A than B" | A > B, strictly |
| "A multiple of 7" | A = 7k for a whole number k |
Worked caselet 1: a warm-up
A college has 200 students in three streams: Arts, Commerce and Science. Science has twice as many students as Arts. Commerce has 40 more students than Arts.
- Let Arts = a. Then Science = 2a and Commerce = a + 40.
- a + 2a + (a + 40) = 200, so 4a = 160 and a = 40.
| Stream | Students | Share |
|---|---|---|
| Arts | 40 | 20% |
| Commerce | 80 | 40% |
| Science | 80 | 40% |
| Total | 200 | 100% |
The ratio of Arts to Commerce is 40 : 80 = 1 : 2. Choosing the smallest group as the variable kept every expression simple.
Worked caselet 2: two months, three categories
In April, a bookseller sold 800 books across three categories: exam guides, fiction and children's books. Exam guides made up 45% of April sales. Fiction sales were 60 more than children's books. In May, total sales rose by 25%. Exam-guide sales in May were 20% higher than in April, and May's children's-book sales were double April's. The rest of May's sales were fiction. Average prices were ₹250 for an exam guide, ₹300 for a fiction title and ₹150 for a children's book, in both months.
Design: categories as rows; April and May as columns.
Translate and solve, sentence by sentence.
- April exam guides = 45% of 800 = 360.
- April fiction + children's = 800 − 360 = 440, and fiction = children's + 60. So 2 × children's = 380: children's = 190, fiction = 250.
- May total = 800 × 1.25 = 1,000.
- May exam guides = 360 × 1.2 = 432.
- May children's = 2 × 190 = 380.
- May fiction = the rest = 1,000 − 432 − 380 = 188.
| Category | April | May | Change |
|---|---|---|---|
| Exam guides | 360 | 432 | +20% |
| Fiction | 250 | 188 | −24.8% |
| Children's | 190 | 380 | +100% |
| Total | 800 | 1,000 | +25% |
Q1. What percentage of May's sales was fiction? 188 ÷ 1,000 = 18.8%.
Q2. By what percentage did fiction sales change from April to May? (188 − 250) ÷ 250 = −62 ÷ 250 = −24.8%, a fall.
Q3. By what percentage did the bookseller's revenue grow from April to May?
- April: 360 × 250 + 250 × 300 + 190 × 150 = 90,000 + 75,000 + 28,500 = ₹1,93,500.
- May: 432 × 250 + 188 × 300 + 380 × 150 = 1,08,000 + 56,400 + 57,000 = ₹2,21,400.
- Growth: 27,900 ÷ 1,93,500 ≈ 14.4%.
Units grew 25% but revenue only 14.4%, because sales shifted from fiction (₹300) to children's books (₹150). A question that asks "why" wants this mix effect.
Q4 (TITA). What was the share of children's books in May's sales, in percent? 380 ÷ 1,000 = 38.
Worked caselet 3: an integer condition
This one was built for this guide and has exactly one solution.
A shop sells gel pens at ₹20, ball pens at ₹10 and fountain pens at ₹50. On one day it sold 40 pens for a total of ₹900. It sold more gel pens than fountain pens, at least one fountain pen, and a number of ball pens that was a multiple of 7.
Step 1: equations. Let the numbers be g (gel), b (ball) and f (fountain).
- g + b + f = 40
- 20g + 10b + 50f = 900, which divided by 10 is 2g + b + 5f = 90
Subtract the first equation from the second: g + 4f = 50, so g = 50 − 4f. Then b = 40 − g − f = 3f − 10.
Step 2: the conditions narrow f.
- b ≥ 0 means 3f ≥ 10, so f ≥ 4.
- g > f means 50 − 4f > f, so f < 10, that is, f ≤ 9.
| f (fountain) | g = 50 − 4f | b = 3f − 10 | b a multiple of 7? |
|---|---|---|---|
| 4 | 34 | 2 | No |
| 5 | 30 | 5 | No |
| 6 | 26 | 8 | No |
| 7 | 22 | 11 | No |
| 8 | 18 | 14 | Yes |
| 9 | 14 | 17 | No |
The unique solution: 18 gel, 14 ball and 8 fountain pens. Check: 18 + 14 + 8 = 40, and 360 + 140 + 400 = ₹900.
Q1. How many gel pens were sold? 18.
Q2. If the "multiple of 7" condition were removed, how many different combinations would be possible? 6 (f from 4 to 9).
Q3. Without that condition, what is the largest possible number of fountain pens? 9, with 14 gel and 17 ball pens. At f = 10, gel pens would also be 10, breaking "more gel than fountain".
This is where caselets meet maxima and minima reasoning: once the equations are set, the questions ask about the range of possible values, and a small table of cases answers all of them.
Common traps
- "More than" read as "at least". In caselet 3, allowing g = f would add f = 10 as a case.
- The wrong base for a percentage. Always ask "20% of what?"
- Missing "the rest". It is an equation, often the last one you need.
- Answering before checking. Re-read every sentence against your finished table; one unused sentence usually means an error.
- Too many variables. Choose the variable that makes the other quantities simple, as with Arts in caselet 1.
Practice set
- In caselet 2, what fraction of the bookseller's May revenue came from exam guides, to the nearest percent?
- In caselet 2, if in June total sales stay at 1,000 and exam guides rise to 480 while children's books stay at 380, how many fiction books are sold?
- In caselet 3, if the shop had instead sold exactly as many ball pens as gel pens (and the other conditions except "multiple of 7" still held), how many fountain pens would it have sold?
Answers:
- About 49%. 1,08,000 ÷ 2,21,400 ≈ 0.488.
- 140. 1,000 − 480 − 380.
- Not possible. b = g means 3f − 10 = 50 − 4f, so 7f = 60, which has no whole-number solution. When a caselet condition gives a fractional count, the scenario cannot happen.
What to do next
- For your next five caselets, draw the empty table before reading any question.
- Tick each sentence as you convert it; never answer while a sentence is unticked.
- Practise three integer-condition caselets this week and write the full case table each time.
- Revisit table-based DI for the fraction benchmarks that speed up the final step.
A note on dates and numbers. Exam patterns, vacancies and schedules change from year to year. Always confirm the current details in the latest notification on the Indian Institutes of Management website .
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