How reasoning questions work

Concepts

One rule, many questions.

Many reasoning questions lean on the same few rules. The alphabet goes round after Z. Every letter has a position. A code can fold the alphabet in half. Learn the rule once and a whole family of questions gets easier.

Each page here takes one rule and tells it as a short story with Kabir and Riya. It works one question, and leaves you three to try.

• Wrapping past ZU, X, A, D, ? looks broken until you remember that after Z comes A. The rule, a worked question, going backwards, and three to try.
• Letter positionsFive anchors, E 5, J 10, O 15, T 20, Y 25, put every letter from C to Z within two steps. The rule, a worked code, and three to try.
• Opposite lettersA code that looks scrambled can be the alphabet folded in half: every letter and its opposite add to 27. The test, a worked code, and three to try.
• Dictionary orderCross out the shared start, compare what is left, and if every letter matches until one word runs out, that word comes first. The rule, a worked list, and three to try.
• The difference tableWrite the gaps, then the gaps of the gaps, until a row settles; extend it and add back up. The rule, a worked series, one floor deeper, and three to try.
• Landmark numbersThe full lists to know on sight: squares to 25², cubes to 10³, powers of 2 to 2¹⁰, factorials to 7!, the 25 primes up to 100. How to spot them in disguise, and three to try.
• Interleaved seriesWhen a series jumps up and down, first check for one rule that alternates; then read odd and even places as two series and count which place the blank is in. The rule, a worked series, and three to try.
• BODMASBrackets, then order (powers and roots), then ÷ and × left to right, then + and − left to right. The shop-counter test, the shared-rung trap, and three to try.