Reasoning · Grade 2-1 Attributes and Reasoning

Problem

Analogical reasoning with figure pairs

Four analogies 'A : B = C : ?': (1) foot : sock = hand : ? (2) a triangle holding a filled circle : a filled triangle holding an empty circle = a circle with two opposite quarters shaded : ? (3) an upright diamond : the same diamond tipped on its side = two squares stacked : ? (4) a triangle holding a small circle : a circle holding a small triangle = a diamond holding a small square : ?. The rule that turns A into B applies unchanged to C. Find the four missing right-hand sides.
Your answer
How to solve
Strategy Look for a Pattern — Each analogy hides a single rule in the first pair. We look for that pattern (what changed from A to B — the relationship, the color, the orientation, the inside/outside swap) and then draw or picture the result of doing the very same change to C.
1STEP 1

Item (1) — find the relationship in words

A sock goes on a foot as a glove goes on a hand, so (1) is glove.

foot → sock → hand → glove
2STEP 2

Item (2) — the colored and uncolored parts swap

Filled and empty trade places, so (2) is the opposite two quarters coloured.

filled⇔empty
3STEP 3

Item (3) — turn the shape a quarter-turn

A quarter-turn makes (3) a wide rectangle of two squares side by side.

rotate 90^°
4STEP 4

Item (4) — the inside and outside shapes trade places

Inside and outside swap, so (4) is a small diamond inside a big square.

outer⇔inner
Answer
(1) glove (2) the opposite two quarters coloured (3) the rectangle turned on its side (4) a small diamond inside a big square
Each answer comes from applying exactly the rule seen in the first pair, so each second pair now shows the same change as its first pair: (1) part-of-body to clothing, (2) colored and empty swapped, (3) turned a quarter-turn, (4) inside and outside swapped. Nothing extra was added or removed, which is what an analogy requires.
Takeaway

Find the one change in the first pair, then do that exact same change to the second pair — that is all an analogy asks!

  • Item (1) — find the relationship in words
  • Item (2) — the colored and uncolored parts swap
  • Item (3) — turn the shape a quarter-turn
  • Item (4) — the inside and outside shapes trade places