If a rectangle were called a circle, a circle a point, a point a triangle and…
2011
If a rectangle were called a circle, a circle a point, a point a triangle and a triangle a square, the shape of a wheel is
Answer: C. Point — Concept. In a renaming (object-substitution) code, a statement of the form "X is called Y" replaces the ordinary name X with the new name Y. The objects…
- A.
Rectangle
- B.
Circle
- C.
Point
- D.
Triangle
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Correct answer: C
Concept. In a renaming (object-substitution) code, a statement of the form "X is called Y" replaces the ordinary name X with the new name Y. The objects themselves do not change — only what they are called. To answer such an item you first name the object in ordinary vocabulary, then find the single statement whose left-hand side is that ordinary name, and report the new name assigned to it. Each substitution is applied exactly once; a new name is never fed back into the table and substituted again.
Application. The question sets up this renaming table:
Ordinary name | New name given by the question |
|---|---|
rectangle | circle |
circle | point |
point | triangle |
triangle | square |
Applying the method to a wheel:
Name the object in ordinary vocabulary. A wheel is round, so in ordinary vocabulary the shape of a wheel is a circle.
Find the statement whose left-hand (ordinary) name is "circle". The question states that a circle is called a point.
Report the new name. In the vocabulary of the question, the shape of a wheel is a point.
Cross-check. The substitution must not be chained. A point is itself renamed to a triangle, but that rule governs objects that really are points; it does not act a second time on the new name just given to a circle. Chaining it would answer the question for a real point instead of for a real wheel. Reading the table the other way confirms the split: "circle" is now the name of a real rectangle, "triangle" is now the name of a real point, and "square" is now the name of a real triangle, so each of those new names belongs to a different object from the round one a wheel actually is.
Result. Under the renaming given, the shape of a wheel is a point.