Chevron Analogy: Rotation or Reflection?
Priya works an analogy item, A is to B as C is to D. The top pair shows a solid black chevron pointing up, with a small dot resting against its outer tip; the second figure is a hollow chevron pointing right, dot against its outer tip still. The bottom pair begins with a hollow chevron pointing down, dot at the outer tip. Five options follow: A solid chevron pointing left with the dot at the tip; B solid chevron pointing down with the dot at the tip; C hollow chevron pointing left with the dot at the tip; D solid chevron pointing up with the dot at the tip; E solid chevron pointing left with the dot tucked inside the V.
Priya marks B. Her explanation: "The first pair flips the shape sideways and swaps the shading. Flip a downward chevron sideways and it still points down, so B." She averages 55 seconds per analogy item in a section that allows 30, and in review she can usually state the rule correctly after seeing the answer key.
1. Give the correct option and demonstrate the rule with a check that Priya did not perform.
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Answer: A. The rule has two parts that both hold on the top pair:
- Rotation, not reflection. A 90-degree clockwise turn takes an up-pointing chevron to a right-pointing one. Check the alternative: a mirror across a vertical line maps an up chevron to an up chevron - never to a right chevron. A mirror across a horizontal line maps up to down. No single reflection produces the observed change, so the transformation must be a rotation.
- Fill inversion. Solid becomes hollow.
Apply that to the bottom pair. A down-pointing chevron turned 90 degrees clockwise points left (down to left, left to up, up to right, right to down). The fill inverts from hollow to solid. The dot, rigidly carried with the shape, stays at the tip. That is option A: solid, pointing left, dot at the tip.
The decisive move is the one Priya skipped - testing whether a reflection could account for the example pair before borrowing the word "flip."
2. Diagnose Priya's error precisely, and explain why her reasoning was internally consistent yet wrong.
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Priya used an undefined verb, "flip sideways," which she silently redefined per figure. On the top pair she treated it as a quarter turn (up to right). On the bottom figure she treated it as a mirror across a vertical axis (down stays down). Two different operations, one label - so her conclusion was forced by her own inconsistency, not by the puzzle.
Her reasoning is internally coherent given that substitution: if flipping really did leave a downward chevron pointing down, B would follow. The failure is upstream. She never anchored the operation to the example, so nothing constrained her choice of flip.
The fix is mechanical and fast: for every analogy, name the operation and then test one rival operation against the first pair. Here, one test - "does a mirror turn up into right?" - eliminates every reflection and settles the item in under five seconds, which also addresses her timing problem. She is not short of reasoning; she is spending her 55 seconds on option comparison instead of on rule verification.
3. Only one example pair is given. Which part of the rule is fully determined by that pair, which part is not, and do the options rescue the item?
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Determined: the rotation amount and direction. Any reflection is refuted outright, and the only rotation taking up to right is a quarter turn clockwise. Fill inversion is also determined - solid appears in figure 1 and hollow in figure 2, with no third fill available.
Not determined: the dot. With a single pair you cannot tell whether the dot is rigidly carried, independently mirrored, or simply redrawn at the tip each time. The pair is consistent with all three.
The options do rescue it - narrowly. A and E differ only in dot placement, and no option shows the dot at the tail. Because the item offers no tail-dot candidate, dot-at-tip is the only reading consistent with some answer, so a well-prepared solver is not penalised. Had a tail-dot option been included, both answers would be defensible and the item would be flawed. Recognising that boundary - a rule can be underdetermined in principle yet safe in practice because of the option set - is exactly the judgement a strong solver applies.