Which one of the following clerks could stock two consecutive aisles?

dre September 3, 2020

same here, I really don't understand the process that guided her to those inferences

Victoria September 13, 2020

Hi @hterhune86 and @dre,

Hopefully I can help clear things up a bit!

We know that there are five clerks in the supermarket: J, K, L, M, and O.

The supermarket has exactly nine aisles.

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

Each aisle is stocked by exactly one clerk. No clerk stocks more than two aisles. As we have five clerks and nine aisles, this means that 4 clerks must each stock two aisles and 1 clerk only stocks one aisle.

This means that none of our clerks can show up more than twice in our linear setup above and only one can show up exactly once.

Now let's go through our conditions.

Rule 1 - O stocks exactly one aisle.

This is helpful because we now know that every other clerk must each stock two aisles.

Rule 2 - K stocks Aisle 2.

Rule 3 - M does not stock Aisle 1.

Therefore, M must stock two aisles out of Aisles 3-9.

Rule 4 - J does not stock consecutive aisles.

This means we can never have two J's next to one another in our linear setup.

Rule 5 - K stocks the only aisle between the two aisles M stocks.

This means that K cannot stock Aisle 9 and M's two aisles can only have one aisle between them that is stocked by K. This gives us an |MKM| block which we must fit in as we know that M cannot stock Aisle 1.

Rule 6 - exactly one of L's aisles is an end aisle.

This means that L must stock either Aisle 1 or Aisle 9 but not both.

Rule 7 - O's aisle is numbered higher than either of K's aisles and lower than at least one of L's. This means that the lowest aisle O can stock is Aisle 6 because K stocks Aisle 2 and the second of K's aisles is trapped within our |MKM| block.

The question stem asks us which of the clerks could stock two consecutive aisles.

We can immediately eliminate answer choice (A) because it directly violates Rule 4 which tells us that J cannot stock two consecutive aisles.

We can also eliminate answer choice (E) because it directly violates Rule 1 which tells us that O stocks exactly one aisle.

Finally, we can eliminate answer choices (B) and (D) because of the |MKM| block. K cannot stock two consecutive aisles because Rule 5 tells us that K stocks the only aisle in between M's aisles. Therefore, one of K's aisles is surrounded on both sides by M and cannot be next to Aisle 2. Rule 5 also means that there must be exactly one aisle in between the two aisles that M stocks; therefore, M cannot stack consecutive aisles.

To prove that answer choice (C) could be true, we just need to find one option where L stocks two consecutive aisles that doesn't violate any of our rules.

If L stocks two consecutive aisles, then L must stock aisles 8 and 9. How do we know this? Rule 6 tells us that exactly one of L's aisles is an end aisle. L cannot stock Aisle 1 and stock two consecutive aisles because Rule 2 tells us that K must stock Aisle 2.

Therefore, one of L's aisles must be the remaining end aisle (i.e. Aisle 9) and the only aisle next to that is Aisle 8.

_ K _ _ _ _ _ L L

We know that O's aisle is higher than either of K's and lower than at least one of L's. We outlined above that the lowest aisle that O could stock is Aisle 6 so let's try that one.

_ K _ _ _ O _ L L

Therefore, our |MKM| block must stock Aisles 3-5, leaving J to stock Aisles 1 and 7.

J K M K M O J L L

Notice that this meets all of our rules:

1) O stocks exactly one aisle: Aisle 6.
2) K stocks Aisle 2.
3) M does not stock Aisle 1 because J does.
4) J does not stock two consecutive aisles because they stock Aisles 1 and 7.
5) K stocks the only aisle (4) in between the two aisles that M stocks (3 and 5).
6) Exactly one of L's aisles is an end aisle (9).
7) O's aisle (6) is higher than either of K's aisles (2 and 4) and lower than at least one of L's (8 and 9).

Hope this helps! Please let us know if you have any further questions.

dre September 22, 2020

Thanks Victoria,it all makes sense now!