Proportion Verification

Measure what is left standing

Counting features cuts most of the field, and everything it leaves behind carries the same features as the object. What is left is size — and size here is a comparison, never a measurement.

The five openings are drawn at one shared scale with each other. One of them fills most of its box and the other four are drawn against that same yardstick, so an opening that sits smaller than its neighbors really is smaller. The object's drawing is not part of that arrangement: it has its own frame, sized to the object. Comparing an opening against the object's drawn size tells you nothing at all. Compare openings to openings, and compare proportions inside a single shape.

Pick a ruler

Do not try to judge absolute lengths. Find the smallest feature on the outline and treat it as your unit, then read every other dimension as a multiple of it.

Here the corner step is the smallest feature and it is one unit square, so the outline reads as eight units wide and four tall — twice as wide as it is tall — with a notch mouth spanning two units, a quarter of the width. This figure is drawn on whole units to keep the arithmetic visible. Real items are not that tidy and do not need to be: "the notch is about a third of the width" and "a bit under twice as wide as tall" are readings you can take by eye, and comparing two of them is all the method ever asks.

Ratios inside one shape

Two comparisons do most of the work: a feature against the whole — notch width against total width — and the whole against itself, height against width. Both are pure ratios, so they are indifferent to how large the drawing happens to be, which is precisely what lets them expose a shape whose parts are wrong relative to each other.

Exact outline

One feature resized

Wrong openings are built from a variant of the object with one feature altered — removed, shifted along its axis, flattened away, or resized as here. A resized feature is what your ratios are for. This outline is still eight units wide and still twice as wide as it is tall, so nothing about its overall size is out of place; but the notch now spans three units instead of two, three-eighths of the width where the object's is a quarter. The internal proportion gives it away and nothing else does.

The copy that is simply too small

Exact outline

A quarter under size

Some wrong openings are a true view of the object copied at 18 to 32 percent under size — shrunk by the same fraction in both directions. Every ratio inside such a shape is correct. The notch is still a quarter of the width, the frame is still twice as wide as tall, the square ruler is still square. No internal comparison can catch it, and hunting for one burns the time the census just bought you.

What catches it is the shared scale. Set it beside the other four openings and it fills visibly less of its box than they do. On the page you never see two outlines superimposed the way the figure above draws them — you see five boxes in a row, and one of them has a smaller drawing sitting in it.

Verify the survivor, not the field

Measuring is slow, so spend it once. When one opening is left, verify that one: check a feature against the whole, check the frame ratio, and check how much of its box it fills against its neighbors. If it holds up, answer and move on — the options you eliminated on the count cannot be rescued by measurement, so they do not deserve a second look. If two survive, measure only those two, and only until they disagree.

The takeaway

Take the smallest feature as your ruler and read the outline in units of it. Test a feature against the whole and the whole against itself, because those ratios expose a feature that was resized while the rest of the shape stayed put. Ratios cannot expose a shape that is uniformly too small — only the openings' shared scale can, so compare openings against each other and never against the object's drawing. Then verify the survivor once instead of re-checking all five. Drill it in the keyholes practice generator.