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Rule out wrong answers

Strategy card

Elimination turns a hard problem into several easy checks.

  1. Step 1: Identify a necessary condition (count, parity, symmetry, sign).
  2. Step 2: Apply it to every option.
  3. Step 3: Repeat with another condition until one option survives.
  4. Step 4: Verify the survivor fully; don't assume.

Tip: Quick checks such as units digits, parity, or symmetry often clear most options fast.

Worked example

Which figure completes the matrix?

blue triangle
outlined blue triangle
striped blue triangle
striped green heart
green heart
outlined green heart
outlined yellow circle
striped yellow circle
question mark, the missing picture?
  • A: striped yellow circle
  • B: blue circle
  • C: yellow triangle
  • D: green circle
  • E: yellow circle (the answer)

Why: Every row has one of each fill (solid, outlined, striped), so the last row needs the one that is missing. Each row keeps its own color (blue, green, yellow, top to bottom). Each row keeps its own shape (triangle, heart, circle, top to bottom). So the missing figure is the yellow circle.

Your turn

Your turn 1 of 3

stanza is to poem as clause is to ___?

stanza→poemclause→?

Your turn 2 of 3

Which number comes next?

8, 27, 64, 125, 216, 343, ?

Your turn 3 of 3

Which figure completes the matrix?

small blue hexagon
small purple hexagon
small red hexagon
2 red hexagons
2 blue hexagons
2 purple hexagons
3 big purple hexagons
3 big red hexagons
question mark, the missing picture?

Keep practicing

Grown-ups: Talk about how detectives and doctors rule things out. Parent guide

Next lesson: Building equations