Caselets

A caselet gives information in sentences. Turn the sentences into a small table or list before solving.

Represent groups as rows and attributes as columns. Translate totals and differences into equations before calculating.

Four pupils choose art and three choose music. Every pupil chooses exactly one club. How many pupils are there? 1. The groups do not overlap because each pupil chooses one club. 2. Add 4 and 3. 3. There are 7 pupils.

The bar is divided into separate art and music groups. Adding 4 and 3 works because every pupil chooses exactly one club, so there is no overlap and no pupil outside these groups. If pupils could choose both, the same addition could count someone twice.

A store sells 100 red and blue pens in two days. Monday sales are 40; Tuesday blue sales are twice Monday blue sales. Total red sales are 55. Let Monday blue be x. Blue total is 45, so x+2x=45 gives x=15. Monday red=25, Tuesday blue=30, Tuesday red=30. Check both day totals and the red total. The same table now answers shares, differences and ratios without rebuilding the reasoning.

Check whether groups can overlap before adding their sizes. Do not add a condition that was never stated, such as equal red sales each day. Preserve unknown cells until a constraint fixes them.

Do not subtract overlapping groups as though they are separate. If someone can belong to both groups, account for the overlap first.

Represent groups as rows and attributes as columns. Translate totals and differences into equations before calculating.

A store sells 100 red and blue pens in two days. Monday sales are 40; Tuesday blue sales are twice Monday blue sales. Total red sales are 55. Let Monday blue be x. Blue total is 45, so x+2x=45 gives x=15. Monday red=25, Tuesday blue=30, Tuesday red=30. Check both day totals and the red total. The same table now answers shares, differences and ratios without rebuilding the reasoning.

Do not add a condition that was never stated, such as equal red sales each day. Preserve unknown cells until a constraint fixes them.

A caselet gives quantitative relationships in prose. Create a table with labelled entities and quantities, then translate the relationships into equations. Keep unknown values explicit rather than inventing them.

Four firms have the following sales and expenses, all in the same monetary unit: A:50,45; B:60,58; C:15,12; D:25,15. Profit equals sales minus expenses, giving 5,2,3,10. Total sales are 150, total expenses 130 and total profit 20. Firm D has the highest profit; B's expenses exceed A's profit by 58−5=53.

Column totals must reconcile: total sales minus total expenses equals total profit. If prose says D's sales are half A's, 25=50/2 checks the relation. A margin uses sales as denominator; a markup or profit-on-cost comparison uses cost. Read the requested base before calculating.

Do not conflate sales with profit or an absolute difference with a percentage. It is often enough to compute the cells needed for the question, but every inferred cell must remain consistent with the case.