PT16.S1.Q23

PrepTest 16 - Section 1 - Question 23

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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.

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23.

A reasoning error in the ████████ ██ ████ ███ ████████

a

attempts to infer █ █████ ████████ ████ ██████ ███████ ████████

b

attributes to every ██████ ██ ███ ██████████ ███ ██████████ ██ ███ ███████ ██████ ██ ███ ██████████

c

fails to take ████ ███████ ████ ██████████ ██ ███ ██████████ ████ ████ ███████

d

ignores the fact ████ ████ ███████ █████ ██ ███ ████ ████████

e

advocates testing people ███ ███████ ███ ████ █████ ██ ██ ██████ ██ ███████ ████ ████ ████ ████ ███████

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