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Hello,

I am doing the prep test 56 and I am stuck in section 1.

Individual hour long auditions will be scheduled for each of six saxophonists-fujimura, Gabrieli, Herman, Jackson, King, and Lauder. The auditions will all take place on the same day. Each audition will begin on the hour, with the first beginning at 1pm and the last at 6pm. The schedule of auditions must conform to the following conditions:

Jackson auditions earlier than Herman
Gabrieli auditions earlier than King does.
Gabrieli auditions either immediately before or immediately after Lauder does.
Exactly one audition separates the auditions of Jackson and Lauder.

I was able to get through question 1-3, and i am not stuck question 4, which is:

The order in which the saxophonist are scheduled to audition is completely determined if which one of the following is true?
a) Herman's audition is scheduled to begin at 4PM
b) Jackson's audition is scheduled to begin at 1pm
c) Jackson's Audition is scheduled t begin at 5PM
d) Lauder's audition is scheduled to begin at 1PM
e) Lauder's audition is scheduled to begin at 2PM

The first question asked for the correct order of the auditions which is:

Jackson, Gabrieli, Lauder, Herman,King, Fujimura. Since this is the case, questions a, and b would seem to be the possible correct answer. but the correct answer is C. Why is that? Since one of the conditions is J_L(Exactly one audition separates the auditions of Jackson and Lauder) wouldnt J be impossible to fit in the 5th spot? Why is question a, and b wrong?

How do you figure out Not laws for the conditions?

Okay, so.

They ask which one would determine all the slots. Firstly, it's important to recognize that the order listed in the first question was one possibility for the order in which they could go, and not the only order in which they could go. You definitely need to make a distinction there.

This is how I worked it out:

If J went fifth and H was after J, the first part of my diagram looked like this:

1.
2.
3.
4.
5. J
6. H

Because the last rule states that exactly one audition separates J and L (and we know that L can't be after J because there are only six slots), L must be in slot 3.

1.
2.
3. L
4.
5. J
6. H

We know that G auditions immediately before or immediately after L does, so he has to be in either 2 or 4 and since we know that his audition is before K's, he cannot be in 4 and therefore must be in 2 (and K must be in 4).

1.
2. G
3. L
4. K
5. J
6. H

The only one left is F, so you put him in at the number one slot and the entire thing is determined.

1. F
2. G
3. L
4. K
5. J
6. H

There is no other way that it could go if J is in the 5th slot. It determines where everything else goes conclusively.

Hope that helps -- I've never tried to explain LG to anyone else before. Heh.

I think you just misread the rule. It's (J _ L) -OR- (L _ J) because the order isn't specified.

Thank you for your answer