Logical and Spatial Reasoning
Core ideas
Logical reasoning tests deductive validity, not truth. Learn to rewrite statements as “if P then Q”, identify the contrapositive (if not Q then not P), and recognise that the converse (if Q then P) is not automatically valid. Syllogism questions require checking whether the conclusion must follow from the premises, even if the premises seem unrealistic. Sequence questions often use differences, ratios, alternating patterns, or squares and primes. Spatial reasoning tests mental rotation, reflection, folding nets, and relative position; use landmarks on the figure and track one feature at a time. Analogies ask for the same relationship, not the same topic.
Traps
The commonest trap is accepting a conclusion that is merely plausible. Others are confusing a mirror image with a rotation, assuming a cube net folds the obvious way, ignoring “all”, “some”, and “none”, and forcing a simple arithmetic rule onto a sequence that alternates. In spatial items, check the handedness of shapes: rotation preserves it, reflection reverses it.
Worked example
Find the next term: 2, 6, 12, 20, ___. Differences are 4, 6, 8, so the next difference is 10 and the answer is 30. Rule of thumb: test differences first, then ratios; if neither is constant, look for a second-level pattern.