#17 - Local, Must Be True

[Dave Killoran]

Complete Question Explanation
(The complete setup for this game can be found here: lsat/viewtopic.php?t=15971)

The correct answer choice is (C)

If there are exactly three oils, in order to conform to the second rule they must be paintings 1-2-3, paintings 2-3-6, or paintings 3-5-6. Thus, the watercolors must be paintings 4-5-6, paintings 1-4-5, or paintings 1-2-4. Accordingly, painting 4 must always be a watercolor and it follows that answer choice (C) is correct.

[boer0140@umn.edu]

Could you possibly walk me through this, please? I can't wrap my head around it at all. I look at it and just go stupid. Thank you!

[Jeff Wren]

Hi Boer,

First, if you haven't already done so, please click on the link that Dave left above for the complete setup for this game. It will help make sure that you're clear on the rules and the diagram.

The question tells us that there are exactly 3 oil paintings and exactly 3 watercolors.

From the initial rules (specifically Rule 7), we know that painting 3 (at the top right of our diagram) is an oil painting, so that is going to be our starting point.

We also know that from Rule 2 that any oil painting must be adjacent to (either horizontally or vertically) another oil painting. In other words, what we can't have is an oil painting that is surrounded by watercolors on all available sides, stranded from the other oil paintings. Each oil painting needs an oil painting buddy (at least one) that is next to, above, or below it.

Since we have exactly 3 oil paintings in this question, they all need to be connected to each other (either in a straight line, such as paintings 1, 2, and 3, or wrapped around a "corner" such as the top right corner (paintings 2, 3, and 6) or the bottom right corner (paintings 3, 5, and 6). If they weren't all connected, at least one of the oil paintings would be "stranded" and surrounded by watercolors.

Because painting 3 is always an oil painting, this limits where the three oil paintings can go in this question to the three possibilities mentioned in the prior paragraph. Basically, painting 3 is an "anchor" to which the other oil paintings must attach. Once you create mini-diagrams for each of these three possibilities, you can fill in the remaining spaces with watercolors (since any painting that is not oil is a watercolor).

Since the question asks for what Must Be True, you need the answer that is true in each possible mini-diagram. In each of the three mini-diagrams, painting 4 is a watercolor (Answer C). None of the other answers is true in each possible diagram.