Numbers and percentages: the LSAT's favorite quiet flaw

This is one of the most reliable flaw families on the test, and it is nearly invisible to a reader going at speed — because the slide it depends on is one everyone makes in ordinary life without consequence.

A percentage is a ratio: a part over a whole. A number is a count. Knowing what happened to one tells you nothing about the other unless you also know what happened to the whole.

The two directions

• Percentage up, number down. A hospital's share of patients who are elderly rose from 20% to 40%, while total patients fell from 1,000 to 300. The count of elderly patients went from 200 to 120 — the share doubled and the number nearly halved.
• Number up, percentage down. A company's security incidents rose from 50 to 80 while its systems grew from 500 to 4,000. More incidents, a much lower rate.

Both are perfectly consistent, and an argument that treats either as a contradiction has committed the flaw. So has one that treats a change in the ratio as evidence about the count.

How the stimulus signals it

Watch the vocabulary on both sides of the argument. Percentage words: rate, proportion, share, percent, per capita, likelihood, incidence, more likely. Count words: number, total, how many, amount, fewer, cases.

The tell is a mismatch — the evidence is in one vocabulary and the conclusion is in the other. Evidence about a rising rate, conclusion about a rising number. That switch, unaccompanied by anything about the size of the whole, is the flaw.

What the argument would need

To move legitimately from a percentage to a number, you need to know the total stayed roughly constant, or moved in a way that does not undo the change. That missing premise is exactly what a Necessary Assumption question is asking for on these, and exactly what a Weaken question attacks — usually by telling you the total moved.

Which makes this family unusually tractable once you see it. The gap is always in the same place, so the answer is always doing the same job.

Two relatives worth knowing

• Percentages of different wholes are not comparable. A higher percentage of a small group can be far fewer people than a lower percentage of a large one, so "more likely" and "more of them" are separate claims.
• Percentage changes compound off a base. A rise from 1% to 2% is a doubling and a one-point change, and an argument can describe the same fact either way to make it sound large or small.

You never need arithmetic on this test. You need to notice which of the two things a sentence is about, and whether the next sentence is still about the same one.