Reasoning, Mental Ability and Basic Numeracy
This domain rewards rule-spotting under time pressure: series, coding, relations, directions, and standard arithmetic shortcuts.
Series and coding
- Number series: test differences first, then ratios, then mixed rules such as multiply by 2 and add 1.
- Letter series: convert letters to positions, A = 1 to Z = 26; remember EJOTY for 5, 10, 15, 20, 25.
- Coding: if TEACHER is written as VGCEJGT, each letter has moved two places forward. Verify on one letter before applying the shift to the whole word.
Arithmetic essentials
Percentage change = (change / original) x 100. Successive changes of a% and b% give a + b + ab/100. Average = sum / count; for the first n natural numbers the average is (n + 1)/2. Simple interest = PRT/100, and compound interest = P(1 + R/100)^T - P.
Worked example
Find the next term: 3, 7, 15, 31, ? Differences are 4, 8, 16, doubling each time, so the next difference is 32 and the answer is 63. Cross-check with the rule multiply by 2 and add 1: 3 gives 7, 7 gives 15, 15 gives 31, 31 gives 63. Two rules agreeing confirm the answer rather than one lucky guess.
Relations and directions
Draw a family tree and mark gender and generation; never assume a sibling link the item does not state. For directions, sketch the path; right-angled turns need Pythagoras, so 3 km east plus 4 km north leaves a displacement of 5 km.
Traps
- Applying a +2 letter shift without wrapping Z back to B.
- Using the new value as the base in a percentage-change question.
- Adding successive percentage changes arithmetically instead of using a + b + ab/100.