Which one of the following, if substituted for the condition that F is discussed earlier than O, and O is discussed e...

Irina on September 11, 2019

@sydneycrudo123,

The substituted condition should result in the same inference as the original condition for it to have the same effect. Let's compare (C) and (D).

F K N O R T are discussed over six weeks. One or more books are summarized.

The following rules apply:

(1) No two books that are summarized are discussed in consecutive weeks.
(2) If N is NOT summarized, both R & T are summarized.

We can infer that if either R or T are not summarized, then N is summarized.

(3) N is discussed earlier than T and T earlier than O

N < T < O

This rule allows us to infer that N cannot be #5 or #6, T cannot be #1 or #6, and O cannot be #1 or #2.

(4) F is discussed earlier than O , and O is discussed earlier than both K & R.

F < O < K
R

Combined with rule (3) we can infer the following chain:

N < T < O. < K
F <. R

We cannot determine the exact positions of N T F except for T cannot be #1, but we can infer that O must be #4 and K &R must be #5 and #6 in some order - KR or RK.

Now the question asks us if we get rid of rule (4) - F < O < K&R chain, which rule would have the same effect.

(D) says O is discussed 4th, and K&R are discussed in consecutive weeks. This rule combined with rule (3) would result in identical inference:

N/T/F > O > K/R

(C) says K & R are among the last three books discussed and F is among the first three books discussed.

Let's see what happens when we combine it with rule (3): N< T < O

If K & R are among the last 3 books discussed they cannot have less than 3 books before them, and if F is among the first three books discussed we know it has to come before K &R , so at the very minimum F N T must come before K &R.

F <. K &R
N < T < O

But this rule does not tell us anything about O, meaning K /R/ O could be in any order as long as they are among the last three books discussed. This rule would allow for:

F N T K R O
F N T K R O
F N T O R K

And so on to be all valid sequences of books discussed. Since the original rule allows us to infer that O is #4 and R & K are #5 and #6 in some order, (C) fails to allow for the same inference, and is therefore, incorrect.

Let me know if this makes sense and if you have any further questions.