Self-study
Support When 100 people who have not used cocaine are tested for cocaine use, on average only 5 will test positive. ██ █████████ ██ █████ ███ ██████ ███ ████ ████ ███████ ██ ████ ████ █████████ █████ ████ █ ████████ ██████ █████ ██ ██████ ██ ██████ ███ ███████ ████ ███ ████ ████████ ██ █████ ███ ████ ████████ ████ ██ ██████ ███ ████ ████ ████████
LSAT Math
The mathematical concept being tested here – the difference between proportions and amounts – occurs enough that it made our list of common flaws. Here’s one example:
If a higher proportion of base jumpers die than car drivers, that doesn’t mean a higher number of people die base jumping than driving.
Unlocking this dynamic usually involves playing around with the sample sizes. In the example above, way more people drive than base jump, so even if a smaller percentage of them die, the overall amount could still be much larger.
That’s what’s happening here. The argument says a higher proportion of cokeheads (99/100) test positive than sobers (5/100), so there must be a higher number of positive-cokeheads than positive-sobers. We mess with this by suggesting there might be way more sobers than cokeheads.
Imagine a world where only 1/100 people are cokeheads:
A random 100-person sample includes 1 cokehead and 99 sobers.
The cokehead would probably test positive (99/100 chance).
Of the 99 sobers, about 5 would test positive (5/100 chance).
In this world, of the 6 people who tested positive, 5 were sobers and only 1 was a cokehead.
Taken individually, these LSAT math questions are pretty difficult. They’re hard to explain from scratch. But they happen often enough that if you take the time to internalize the general approach, solving them becomes routine.
23.
A reasoning error in the ████████ ██ ████ ███ ████████
a
attempts to infer █ █████ ████████ ████ ██████ ███████ ████████
(A) points to a different common flaw that doesn’t happen here – the value judgment. It is indeed inappropriate to infer normative conclusions (about how things ought to be) from merely descriptive premises (about how things are).
The stimulus never uses normative language, though. All its claims are descriptive.
b
attributes to every ██████ ██ ███ ██████████ ███ ██████████ ██ ███ ███████ ██████ ██ ███ ██████████
Applying (B) to the stimulus, there needs to be a property that does apply to people on average, which the stimulus then tries to apply to every individual person. Like “iguanas are 12in long on average, so all the zoo’s iguanas must be 12in long.”
The stimulus never makes a jump between statistical figures and individual applications. All its claims, including the conclusion, are about what we can expect “on average.”
c
fails to take ████ ███████ ████ ██████████ ██ ███ ██████████ ████ ████ ███████
If you’re familiar with LSAT math questions, (C) fits the mold well enough that you don’t even need to spend time noodling out hypothetical situations. “What if the sample sizes are super different?” is the archetype for solving percent vs. amount puzzles.
The hypothetical we discuss in the analysis section – which features a very low proportion of cokeheads in the population – serves as a counterexample to the argument’s conclusion. It’s a scenario in which the majority of people who tested positive were not cokeheads.
Change the proportion of cokeheads to sobers, though, and you get a different situation. If there are equal numbers of cokeheads and sobers walking around, a random sample would yield more positive-cokeheads than positive-sobers.
d
ignores the fact ████ ████ ███████ █████ ██ ███ ████ ████████
Far from ignoring it, the argument
e
advocates testing people ███ ███████ ███ ████ █████ ██ ██ ██████ ██ ███████ ████ ████ ████ ████ ███████
(E) points to a different common flaw that doesn’t happen here – the value judgment. It is indeed inappropriate to infer normative conclusions (about how things ought to be) from merely descriptive premises (about how things are).
The stimulus never uses normative language, though – it never advocates anything. All its claims are descriptive.