Caselets

At a glance 9 rules

1. 1Question first, then gridRead the question line first, then put the paragraph into a grid: groups down, attributes across, totals in the last row and column.
2. 2The rest'The rest', 'remaining' and 'others' are the total minus every stated part; work them out before you use them.
3. 3Check the baseAsk what each percent or ratio is of: '40% of those shortlisted' or '25% fewer than Stall A' is not a share of the whole.
4. 4Fill by levels$\text{count} = \text{total} \times s_1 \times s_2$$s_k = \text{share at level } k$
5. 5The grid closesIn a two-way grid (boys and girls by hostel and day), the row totals, the column totals and one inside cell fix every other cell.
6. 6All three, at least$\text{in all three} \ge A + B + C - 2N$$A, B, C = \text{group sizes},\ N = \text{total}$
7. 7Push to the extremesTo make one group's count as small as possible, fill every other group to its limit first; whatever is left over is the minimum.
8. 8Track one quantityWhen things move in and out (books, stock, money), track the one figure that changes; the other is the fixed total minus it.
9. 9Split from two totals$\text{dearer count} = \dfrac{\text{money} - \text{count} \times \text{low price}}{\text{high price} - \text{low price}}$