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Why Missing-Number Figures Are Free Marks
Almost every reasoning section — SSC, Railway, and the Mental Ability part of BPSC TRE-4 — carries one to three questions where numbers sit in a grid, a wheel or a set of triangles, and one of them is replaced by '?'. They look like guesswork, but setters draw on a small toolkit of rules: sums, products, squares, cubes and cross-multiplication. The skill is not brilliance; it is testing those rules in a fixed order instead of staring at the figure.
The one rule that decides everything: a pattern counts only if it works on every complete row, column or figure. A rule that fits one row and fails the next is a coincidence, and setters deliberately plant such coincidences to trap students who stop checking too early.
1. Find the missing number. Row 1: 5, 3, 16 Row 2: 7, 4, 22 Row 3: 6, 9, ?
2. In a wheel, the numbers 2, 3, 4 and 5 sit in four sectors, and directly opposite them are 8, 27, 64 and ?. Find ?.
3. In each figure, four corner numbers (top-left, top-right, bottom-left, bottom-right) surround a centre. Figure 1: 9, 2, 3, 4 → centre 30 Figure 2: 8, 5, 2, 7 → centre 46 Figure 3: 6, 3, 4, 9 → centre ?
4. Each triangle has three corner numbers and one number inside. Triangle 1: corners 1, 3, 2 → inside 36 Triangle 2: corners 2, 4, 1 → inside 49 Triangle 3: corners 3, 2, ? → inside 64 Find ?.
5. Find the missing number. Row 1: 4, 6, 8 Row 2: 3, 5, 2 Row 3: 11, 29, ?
6. While solving a 3 × 3 number grid, you find a rule that fits the first row but not the second. What should you do?
7. Each circle is divided into four sectors with a number in the centre. Circle 1: 5, 8, 6, 11 → centre 30 Circle 2: 3, 9, 12, 6 → centre 30 Circle 3: 7, 10, ?, 4 → centre 30 Find ?.
8. Find the missing number. Row 1: 5, 7, 18 Row 2: 6, 11, 25 Row 3: 8, 15, ?