The Fixed Answer Scale

Five choices that never move

Every cube counting item offers five choices. In the items you will drill here, those five are always the same ladder, in the same order, item after item: 1 cube, 2 cubes, 3 cubes, 4 cubes, 5 cubes.

No other PAT section hands you the answer set in advance. Keyholes redraws five apertures every time; cube counting reuses one scale for the whole section. Everything in this topic follows from that, so treat it as the way these items present their choices — dependable here, and worth exploiting every time you see it.

The position is the answer

Because the ladder is fixed and ordered, the count you arrive at tells you the letter without any searching. Two cubes is choice B. Three cubes is always choice C. You never read the options at all — you count, then move your hand to the position that count occupies.

How many cubes have one of their exposed sides painted?

A

1 cube

B

2 cubes

C ✓

3 cubes

D

4 cubes

E

5 cubes

That item asks how many cubes have one of their exposed sides painted. The class holds three cubes, so the answer sits at C. Notice how easily those two numbers could be confused: the question's number is one, and the answer is three. They are different quantities, and the section leans on that confusion.

The scale checks your work for free

The ladder stops at 1 and at 5, and in these items the asked class always falls inside that range: a number of painted sides is only put to you when the pile holds between one and five cubes with it. That gives you a self-check that costs nothing.

If your count for the asked number comes out as 0, or as 6 or more, you have miscounted. No arithmetic is needed to know it — nothing on the scale matches, so the error is yours and it is already proven. Zero usually means you missed a class of cube entirely; six or more usually means you counted cubes that belong to a neighboring class.

Seven cubes, each badged with its painted-face count. Asked for cubes with exactly three painted sides, you count the tinted ones: three of them, so the answer is C. Asked instead for four painted sides on this same pile, you would find exactly one cube and answer A. Both counts sit comfortably inside the scale — as they must.

Zero is real, but it is never asked

Cubes with no painted faces at all genuinely exist. Bury a cube deep enough in a large pile and every one of its five paintable faces meets a cemented neighbor, leaving it entirely unpainted inside the block.

But no question ever asks for that class. The prompts in this section run from one painted side to five, and the choices count cubes from 1 to 5. So a fully enclosed cube is real, it is part of the pile, and it never belongs to the class you are being asked about. Keep it in the pile and out of your answer.

Read the number word, not the digit

The question spells its target out as a word — "how many cubes have two of their exposed sides painted?" — while the choices use digits. That mismatch is deliberate protection, and it is also the section's cheapest error: seeing "two" in the question and reaching for B.

Say both numbers to yourself before you answer. The question asks about two painted sides. My count is four cubes. Four is D. One sentence, and the entire family of misreads disappears.

The takeaway

The five choices are the fixed ladder 1 through 5 cubes, so position is the answer and three cubes is always C. Your count for the asked number lands inside 1 to 5; a tally of 0 or of 6 or more is proof you miscounted, caught before you have looked at a single option. Unpainted cubes exist inside piles but are never the class in question, and the number in the prompt is a count of painted sides, never a count of cubes.