Caselet DI for LIC AAO

A caselet gives you the data as a paragraph instead of a table or chart. Every number you need is in there, but it is hidden inside sentences like "two-thirds of the term policies" and "the rest were health policies". Caselets feel slow because candidates try to answer each question straight from the paragraph and end up re-reading it five times. The fix is simple: turn the paragraph into a table first, then answer every question from the table.

The method

1. Read the paragraph once, fully. Do not calculate yet. Note what the categories are: products, cities, men and women, online and offline.
2. Draw an empty table. Rows for one category, columns for the other, with a Total column. Leave cells blank.
3. Fill in what is given directly, then fill in what can be calculated, in the order the paragraph allows.
4. Check the totals. Every row and column should add up. If they do not, one number was applied to the wrong base.
5. Answer from the table. Now each question is a table question: a lookup, a percentage or a ratio.

Why this works: the paragraph is written in the order that is easiest to write, not the order that is easiest to use. The table puts every value in one place, so each question takes one step instead of a re-read.

Wording that changes the base

Worked caselet 1: policies sold by an agent

An agent sold 240 policies in a year: term, endowment and health policies. Term policies made up 40% of the total. The number of endowment policies was two-thirds of the number of term policies. The rest were health policies. A quarter of the term policies were sold online. (Made-up data.)

• Term = 40% of 240 = 96.
• Endowment = 2/3 × 96 = 64.
• Health = 240 − 96 − 64 = 80.
• Term online = 96 ÷ 4 = 24; term offline = 96 − 24 = 72.

Questions:

1. How many health policies were sold? 80.
2. What is the ratio of endowment to health policies? 64 : 80 = 4 : 5.
3. How many term policies were sold offline? 72.
4. What percentage of all policies were health policies? 80 ÷ 240 = 1/3 = 33.33%.

Worked caselet 2: agents in three cities

A branch recruited 180 agents in three cities, X, Y and Z. Y had 20 more agents than X, and Z had twice as many as X. In X, 45% of the agents were women. In Y, the ratio of men to women was 7 : 5. In Z, three-eighths of the agents were women. (Made-up data.)

Let X have a agents. Then Y = a + 20 and Z = 2a.
a + (a + 20) + 2a = 180, so 4a = 160 and a = 40.
X = 40, Y = 60, Z = 80.

• X: women = 45% of 40 = 18; men = 22.
• Y: women = 5/12 × 60 = 25; men = 35.
• Z: women = 3/8 × 80 = 30; men = 50.

Check: 107 + 73 = 180, and each row adds up.

Questions:

1. How many women agents were recruited in all? 73.
2. What percentage of the agents in Z were men? 50 ÷ 80 = 62.5%.
3. What is the ratio of men in X to women in Z? 22 : 30 = 11 : 15.
4. Women in Y were what percentage of all women agents? 25 ÷ 73 × 100 = about 34.2%.
5. If 20% of the men in Z left, how many agents would remain in Z? 20% of 50 = 10, so 80 − 10 = 70.

Worked caselet 3: overlapping cover

Of 300 policyholders at a branch, 180 have a life cover and 140 have a health cover. 60 have both. (Made-up data.)

Overlap caselets are best drawn as a two-circle diagram, or as a small table.

• Only life = 180 − 60 = 120.
• Only health = 140 − 60 = 80.
• At least one = 120 + 80 + 60 = 260.
• Neither = 300 − 260 = 40.

Q. How many policyholders have exactly one of the two covers? 120 + 80 = 200.

More traps

• Applying a percentage to the total when the sentence says "of the term policies".
• Stopping before the "rest" is found, then treating a missing value as zero.
• Reversing a ratio given "respectively".
• Getting a fraction of a person or a policy. That is a signal that a base is wrong. Re-read the sentence.

Practice set

1. In caselet 1, if 25% of endowment and 40% of health policies were also sold online, how many policies were sold online in all? 72. Term 24 + endowment 16 + health 32.
2. In caselet 2, how many men were recruited in all? 107. 22 + 35 + 50.
3. In caselet 2, what percentage of the agents in X were men? 55%. 22 ÷ 40.
4. In caselet 2, by what percentage did women in Z exceed women in X? About 66.7%. (30 − 18) ÷ 18 = 2/3.
5. In caselet 3, what percentage of policyholders have exactly one cover? About 66.7%. 200 ÷ 300.
6. In caselet 3, what is the ratio of "only life" to "neither"? 3 : 1. 120 : 40.
7. In caselet 3, what fraction of those with health cover also have life cover? 3/7. 60 ÷ 140.
8. In caselet 1, if next year term policies rise by 25%, health falls by 10% and endowment is unchanged, what is the new total? 256. 120 + 64 + 72.

What to do next

• For the next five caselets you solve, draw the table before reading a single question.
• Time yourself: aim for the table in about two minutes and the questions in four.
• Revise percentages on different bases in percentage for LIC AAO and ratios in ratios and averages.
• If tables themselves are slow, practise table DI first.