Q2117 Honor Roll Students

[kenyamlee]

Here is the question:
I now know the answer and it makes sense intuitively I don't know the
strategy of how to arrive or test the answers.

Here is the question:
20% of honor-roll students have GPAs of at least 3.9, and 80% of honor-roll
students have GPAs of at least 3.7.

Here are the choices:
-20% of honor-roll students have GPAs below 3.7.

OR

Every honor-roll student has a GPA of at least 3.7 or at least 3.9.

[ohthatpatrick]

Proving the correct answer is easy. Not getting tricked by the trap answer is harder.

Proving the correct answer:

80% of honor roll are 3.7 or higher.

Okay, so 20% of honor roll is below 3.7

Done.

You don't even need the other fact to derive the correct answer.

If I say 60% of my friends are guys, then you immediately know that 40% of my friends are not guys.

How did they think we wouldn't get that?

Well, they put in a 20% fact of their own to entice us into confusion.

80% of HR get at least 3.7
20% of HR get at least 3.9

This is designed to make your brain think that THESE two groups complete 100%.

But that's incorrect.

The 2nd group is a subset of the 1st group.

Say that Billy has a 4.0 GPA and is on the HR.

Is he part of the 80% of HR who have at least 3.7?

Yes, he's got at least 3.7

Is he part of the 20% of HR who have at least 3.9?

Yes, he's part of that as well.

So everyone in the 20% with at least 3.9 was ALSO counted in the 80% with at least 3.7

What these statistics could collectively give us is this:
20% .. below a 3.7
60% .. 3.7 - 3.9
20% .. 3.9 or higher
==========
100%

If you add up the last two groups, you get that 80% had a 3.7 or higher.

Make sense?