How reasoning questions work

Reasoning concepts

One rule, many questions.

Some reasoning questions lean on a rule you can learn once. 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 ZLetter series such as U, X, A, D, ? go round the corner: after Z comes A. The rule, a worked question, counting back past A, and three to try.
• Letter positionsFind any letter’s position in the alphabet without counting from A. Five anchors, EJOTY (E 5, J 10, O 15, T 20, Y 25), a worked code, and three to try.
• Opposite lettersOpposite letters in coding-decoding: A and Z, B and Y, every pair adds to 27. The test for a code that looks random, a worked code, Atbash, three to try.
• Dictionary orderArrange words in dictionary order: cross out the shared start and the first different letter decides. A word that runs out first comes first. Three to try.
• The difference tableStuck on a number series? Write the gap between each pair of numbers, then the gaps of the gaps. A worked question, going one row deeper, three to try.
• Landmark numbersWhen a number series looks almost familiar, check the nearest square, cube, power of two, factorial or prime. A worked question, and three to try.
• Interleaved seriesIf the gaps jump up and down, first check for one alternating rule; if none, read odd and even places as two series and find the blank. Three to try.
• BODMASThe BODMAS rule: brackets, then order (powers and roots), then ÷ and × left to right, then + and − left to right. The shop-counter test and three to try.
• Operator substitutionWhen + means × and ÷ means −: write the new line under the printed one, read each sign once, then solve with BODMAS. Other disguises, and three to try.
• The shift cipherIn a letter-shift code every letter moves the same number of places. Find the step, check it on every letter, then move them all. Three to try.
• All, Some, NoSolve syllogisms by drawing circles: All is inside, Some overlaps, No is apart. A conclusion follows only if it holds in every drawing. Three to try.
• Rank from both endsRank from the left plus rank from the right counts the person twice, so total = left + right − 1. The other end, who stands between, three to try.
• The clock angleAngle between the hands = 30 × H − 5.5 × M, ignoring a minus sign; over 180°, take it from 360°. Why the hour hand creeps, a worked question, three to try.
• Mirror timeTo read a clock in a mirror, take the mirror time from 11:60: minutes from 60, hours from 11. The two edge cases, a worked question, and three to try.
• Odd daysWhole weeks change nothing: divide the days by 7, and the remainder, the odd days, moves the weekday. Months, leap years, centuries, and three to try.
• Rotation is not reflectionIs the figure turned, or mirrored? A turn keeps left as left; a mirror swaps left and right. Walk from feature to feature. Water images, three to try.

See the topics these rules belong to →