Your Percentage Went Up. Did the Number? The LSAT Is Betting You Won’t Check.
Here is a sentence that sounds airtight: “This year a larger percentage of our budget went to research, so we are spending more on research.”
Read it again slowly. Does the conclusion actually follow?
It doesn’t, and the LSAT knows you will probably accept it anyway. This is the percent-versus-number flaw, and it shows up in flaw, weaken, and even must-be-true questions often enough that it is worth training your eye for it.
A percentage is a share of a total. A number is a count. They are different kinds of information, and the LSAT loves arguments that start with one and end with the other without ever mentioning the total that connects them.
Take the budget example. Suppose last year the company spent $10 million total, with 10% going to research. That is $1 million. This year the company had a rough year and spent only $4 million total, with 20% going to research. The percentage doubled. The dollar amount fell from $1 million to $800,000. The premise is true and the conclusion is false, which is exactly what a flawed argument looks like.
The flaw runs in the other direction too. “We hired more engineers this year, so engineers are a bigger share of our staff.” If the company hired a hundred people and only ten were engineers, the number of engineers went up while their share of the company went down. Same mistake, reversed.
Why do smart people miss this? Because the two ideas feel like they travel together. When a share goes up, our intuition says the thing itself must have grown. Usually that intuition is fine in everyday life, where totals tend to stay roughly stable. The LSAT builds its arguments in exactly the places where that assumption breaks.
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So here is the habit I teach. Whenever a premise talks about a percentage, proportion, or rate, and the conclusion talks about a number or a count (or the reverse), stop and ask two questions. Do I know the total? Did the total stay the same? If either answer is no, the inference is exposed, and you have found the gap in the argument.
That habit does different jobs depending on the question type.
On a flaw question, the correct answer will usually be a phrase like “confuses a change in percentage with a change in absolute number,” or it may describe the same error in more abstract language, such as treating a change in proportion as evidence of a change in quantity. Know that the abstract version exists so it doesn’t throw you.
On a weaken question, your job is easy once you see the flaw. You want the answer that says the relevant total changed. If a new study shows the overall number of accidents fell sharply, then “a higher percentage of accidents involved new drivers” no longer implies more accidents involving new drivers. The percentage and the count can move in opposite directions.
On a strengthen question, you do the reverse. The best answer is often the one that tells you the total stayed the same, because that is the missing piece that makes a percentage legitimately stand in for a count.
There is a narrow case where going from percentage to number is perfectly valid: when the total is given and held constant. If a town has exactly 5,000 residents both years and the share of residents who bike to work rises, then the number of bikers did rise. The LSAT occasionally uses this as a trap in the other direction, so don’t memorize “percent to number is always flawed.” Memorize “percent to number needs the total.”
One more place this hides is in answer choices. A wrong answer in a must-be-true question might take a percentage-based statement and draw a numerical conclusion from it. If you have trained yourself to flag that jump, you will cross out those choices in seconds.
A quick drill you can do without any materials: next time you read a news headline with a statistic, ask whether it is a share or a count and whether the total could have moved. “Crime rate up 10%” and “crimes up 10%” are not the same claim. You will start noticing the swap everywhere, and that is the point. The LSAT is mostly a test of whether you notice small gaps that other people read past.
I originally published the complete version of this framework on Verbloom: https://verbloom.dev/blog/percent-vs-number-flaw-lsat
