There are exactly seven houses on a street. Each house is occupied by exactly one of seven families: the Kahns, Lowes, Muirs, Newmans, Owens, Piatts, Rutans. All the houses are on the same side of the street, which runs from west to east.

- The Rutans do not live in the first or the last house on the street.
- The Kahns live in the fourth house from the west end of the street.
- The Muirs live next to the Kahns.
- The Piatts live east of both the Kahns and the Muirs but west of the Lowes.

- Which one of the following families could live in the house that is the farthest east?

- the Kahns
- the Muirs
- the Newmans
- the Piatts
- the Rutans

- Which one of the following families CANNOT live next to the Kahns?

- the Lowes
- the Newmans
- the Owens
- the Piatts
- the Rutans

- If the Muirs live west of the Kahns, then the Rutans CANNOT live next to both

- the Kahns and the Piatts
- the Lowes and the Piatts
- the Muirs and the Piatts
- the Muirs and the Owens
- the Muirs and the Newmans

- If the Newmans live immediately west of the Kahns, which one of the following statements must be false?

- The Owens live next to the Newmans.
- The Owens live next to the Rutans.
- The Piatts live next to the Lowes.
- The Piatts live next to the Muirs.
- The Rutans live next to the Newmans.

- If the Owens live east of the Muirs, which one of the following statements must be true?

- The Kahns live east of the Muirs.
- The Kahns live west of the Rutans.
- The Owens live west of the Lowes.
- The Owens live east of the Piatts.
- The Owens live west of the Piatts.

- If the Owens live east of the Kahns, which one of the following pairs of families must live next to each other?

- the Kahns and the Piatts
- the Lowes and the Owens
- the Muirs and the Newmans
- the Newmans and the Rutans
- the Owens and the Piatts

**The Action:** A fairly straightforward sequencing set, with a very minor wrinkle: the use of the terms “west” and “east” to refer to the different sides of the sequence. We’re asked to order seven families (K, L, M, N, O, P, and R) in seven houses lined up west (left) to east (right) on one side of a street. The Key Issues are:

1) Which families can, must, or cannot occupy which house?

2) Which family can, must, or cannot occupy a house adjacent to what other family?

**The Initial Setup:** Keep this setup simple; seven dashes or the numbers 1 to 7 from left to right on your page will suffice. You may wish to jot down a “W” to the left and an “E” to the right of the sketch, just for good measure, to remind you which side is which. List the roster of families off to the side, and you’re ready to fill the Rules into this basic setup:

**The Rules:**

2) Once again, the most concrete rule first: The Kahns live in the fourth house from the west. Don’t let the awkward wording throw you. This simply means that the Kahns live in house 4, so put that directly into the sketch.

1) “No R” over houses 1 and 7 should help us keep this in mind.

3) Since the Muirs live next to the Kahns, who live in house 4, the only possible houses for the Muirs are 3 and 5. Place an “M” with arrows pointing to houses 3 and 5 into your sketch.

4) Since the Kahns live in house 4, this rule tells us that the Piatts can only live in houses 5, 6, or 7. But the Piatts can’t live in 7, because the Lowes must live to the east (right) of them. So the “P . . . L” chunk will have to fall somewhere within houses 5, 6, and 7. Jot that down, and we’re ready to move on.

**Key Deductions: **

There’s no major deduction here, but there are only a limited number of ways the sequence could play out. It’s therefore worth quickly exploring the possibilities: M lives in either 3 or 5. Let's say M occupies the 5th house. Since the P. . . L pair must be east of K, we get this:

R, O, and N are left to fill in the 1,2 and 3 houses. R, you remember, can't be on either end, so that family would be in either 2 or 3 in this situation, leaving O and N for the other spots, in either order.

The second scenario is a little more flexible, and arises if we instead place M 3rd. P and L still need to be to the right of K, and must still maintain that K..P..L ordering. The other 3—N, O, and R—would fill the remaining spots, so long as R isn't first or last. This ordering isn't as determined as the other, and naturally doesn't help us as much, but it's still good to consider the possibilities in advance, which we've done.

**The Final Visualization:** Here’s what we’re armed with to tackle the questions:

**The Questions:**

**1. (C)**

The Lowes live in house 7 in our first possibility above, but that’s not a choice. (A), (B), (D), and (E) directly violate Rules 2, 3, 4, and 1, respectively, which leaves only (C). A glance at our sketch would quickly confirm the same result.

**2. (A)**

This one’s also pretty much a gimme. We can easily infer from Rule 4 that the Piatts live between the Kahns and the Lowes. Therefore, there’s no way that the Kahns can live next to the Piatts. The rest of the families in (B) through (E) can live next to the Kahns.

**3. (C)**

The info in the stem puts M in house 3, which conjures up the second scenario we discussed earlier. This was the less helpful scenario, so let’s check out the choices.

(A) R can live next to both K and P: K in 4, R in 5, P in 6, and L in 7, with N and O floating between 1 and 2.

(B) is possible too: M,K,P,R,L in 3 through 7, again with N and O floating at the beginning.

(C) M is in house 3, K is in 4, and P is either in 5 or 6. It’s therefore not possible for the Rutans to live between the Muirs and the Piatts, making (C) our answer.

(D) and (E) Either O or N can live in house 1, and with R in 2 and M in 3, so both of these are possible.

**4. (A)**

N in 3 points us to our first scenario:

We’re left with R and O for houses 1 and 2, and Rule 1 forces R into house 2 and O into house 1. The entire setup of families to houses is complete: O, R, N, K, M, P, L. The Owens clearly do not live next to the Newmans. Choice (A) it is.

**5. (A)**

Here we can deduce that the second scenario above is operative: The only way for the Owens to live to the east, or right, of the Muirs, is for M to live in 3, with O, P and L fitting somewhere in 5, 6, and 7. The two remaining entities, N and R, will therefore take houses 1 and 2, respectively (R can’t take 1 from Rule 1). The choice that corresponds to this is (A): K must be east of M. (B) is false, and (C) through (E) are possible only.

**6. (D)**

The testmakers liked question 12 so much, here it is again (nearly). So we should consult the same sketch as the one for number 12: M is in 3, K is in 4, O, P, and L are relatively free to float between spaces 5, 6, and 7 (as long as P is before L), N is in house 1, and R is in house 2. Scan down the list for adjacent families; N and R must live next to one another, specifically in houses 1 and 2, respectively. (A), (B), and (E) contain pairs that are possible neighbors, but need not be, whereas the pair in (C) are definitely separated by the Rutans.

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