q2202 among certain group of teachers

[yoohoo081]

How is it that no teachers had more experience than lovejoy and not some?
Is this because albright is included into livejoy? This was explanation my financial friend explained.

[noah]

Let's see the question text - there's a lot of similar questions, and our numbering system is not what it used to be.

[yoohoo081]

Question: Among a certain group of teachers Mrs. Albright has more experience than all but 2 of her colleagues, and Mrs. Lovejoy has more experience than all but 3 of her colleagues.

1. Some teacher has more exp than Lovejoy but less exp than Mrs. Albright

2. No teacher has more experience than Mrs. Lovejoy but less exp than Mrs. Albright

So, Is #1 correct because... (see diagram below)

L-> A-> xx
------------->(experience)
L= lovejoy
A= Albright
xx= other teachers

[noah]

I think it's easier to approach this considering the numbers:

A: 6 years exp.

And, in order to have there be just two more with experience than L, we can put:

#1: 7 years
#2: 8 years

Now, we need to have L have 3 people with more experience, so how many years should we assign her?

If we assign her 6, like A, there would be only two with more experience, and if we assign her more than 6, we'd definitely not get our 3 more experienced folks. So we have to assign her 5 or some other lower number. Now, A has 3 people with more experience: #1, #2, and L. There can't be anyone else in that group because then there would be more than 3 with more experience than A.

That's why the answer is that "No teacher has more experience than Mrs. Lovejoy but less experience than Ms. Albright." (You had listed the wrong correct answer.) We can't validly put someone with an experience number that's between A and L's. Watch:

A:6
#1: 7
#2: 9
L: 8

Nope! We need 3 colleagues with more than L, not 1!

A: 6
#1: 7
#2: 9
#3: 5

L: 4

Nope! We need 3 colleagues with more than L, not 4!

BTW, thanks to Zagreus for pointing out an egregious error in the first version of this!