Which one of the following is a pair of clerks, neither of whom could stock aisle 5?

Irina August 22, 2019

@Venella-Vellanki,

The question is asking which clerks CANNOT stock aisle 5.

I am posting the explanation below, but if you would like to try it yourself first, feel free to come back to it later.

The game requires us to assign J K L M O to 9 isles, 1-9. Each aisle is stocked by one clerk and no clerk stocks more than two aisles:

___ ___ ___ ___ ___ ___ ___ ___ ___
1 2 3 4 5 6 7 8 9

The following conditions apply:

(1) O stocks exactly 1 isle.
This rule tells us that everyone else stocks 2 because there are 4 clerks left to stock 8 isles and no clerk can stock more than 2 aisles.

(2) K stocks aisle 2
K = 2

(3) M does not stock aisle 1
M = ~1


___ K ___ ___ ___ ___ ___ ___ ___
1 2 3 4 5 6 7 8 9
~M

(3) J does not stock consecutive aisles, so she could not stock 3 & 4 or 5& 6 for instance. Let's remember this condition for now.

(4) K stocks the only aisle between the two aisles M stocks.

This rule gives us the following pattern: M K M. Since we know that one of the aisles K stocks is #2 per rule (2), and there is only left and it must be between two Ms, K cannot be #9.

___ K ___ ___ ___ ___ ___ ___ ___
1 2 3 4 5 6 7 8 9
~M ~K

(5) Exactly one of L's aisles is an end aisle.

This rule tells us that one of L's aisle is either 1 or 9, but L cannot be in both #1 and #9.

___ K ___ ___ ___ ___ ___ ___ ___
1 2 3 4 5 6 7 8 9
~M ~K
/L /L

(6) O's aisle is numbered higher than any of K's aisles, and lower than at least one of Ls.

We know that K is in aisle #2 and the other K is a part of MKM pattern per rule (4), so the lowest possible aisle the second K could be is #4 if the order is ? K M K M. This means O cannot be in any aisle lower than aisle 6. Since O must be lower than at least 1 one of Ls, O cannot go on aisle #9 either. We can thus infer that O must be in either aisle 6, 7, or 8.
/L /O /O /O /L
___ K ___ ___ ___ ___ ___ ___ ___
1 2 3 4 5 6 7 8 9
~M ~O ~O ~O ~O ~K
~O ~O
~M

This rule also tells us that M cannot be in aisle #9 because O must come after the MKM pattern.

Now the question asks which clerks cannot stock aisle #5.

We can tell from our initial setup that one of them is O, so we can eliminate all the answer choices that fail to include O - (A), (C) and (D). Let's look at (B) and (E).

(B) K and O.

If K stocks 5, then M must stock 4 and 6, then L could be #1, J #3 and #9, O #7 and L #8. This order complies with all the rules, thus we can eliminate (B).

L K J M K M O L J
1 2 3 4 5 6 7 8 9

(E) L and O

If L stocks 5, the only aisles we could fit MKM are 678 as we know M cannot be #9 per our inference from rule (6) above. If MKM is 678, O must be #9 but then we have no space left for at least 1 L that must come after O per rule (6). We can thus conclude that L cannot be #5, and (E) is the correct answer choice.


L K L M K M O
1 2 3 4 5 6 7 8 9

Does this make sense?

Let me know if you have any further questions.