Pattern guide

XOR Questions

XOR — exclusive-or — is the most common composition mechanic on real assessment tests. Shared elements cancel, exclusive elements survive. The solver applies a symmetric difference.

What this pattern means

Row 2 contains exactly the elements that appear in row 0 OR row 1 — but not both. Elements that appear in both parents cancel out. XOR is symmetric (swapping row 0 and row 1 gives the same result), which distinguishes it from subtraction.

How to spot it

  • Two parent cells share some elements and differ on others.
  • Row 2 looks 'sparser' than the union of the two parents.
  • Elements present in exactly one parent always carry through.

Common visual signals

  • Dot-pattern or line-grid questions where elements cancel.
  • Cells whose union would be 'crowded' but whose actual content is thinner.
  • A clear cancellation step when comparing parents element by element.

Step-by-step solving tactic

  1. 1List the elements present in row 0 and row 1 cells of the column.
  2. 2For each element, check 'is it in both?' If yes, drop it.
  3. 3Elements in exactly one parent appear in row 2.
  4. 4Confirm by re-applying the rule to a different row.

Common traps

  • Confusing XOR with union (OR) — union keeps shared elements; XOR drops them.
  • Confusing XOR with subtraction — XOR is symmetric, subtraction is not.
  • Misidentifying which elements are 'shared' when positions differ slightly.

Related patterns

Apply this pattern under timed conditions

Take the free 10-question matrix reasoning practice test — every question carries the xor pattern or another commonly tested mechanic.

Free test · 10 questions