There are five houses on each side of a street, as shown in the figure above. No two houses next to each other on the same side of the street and no two houses directly across from each other on opposite sides of the street can be painted the same color. If the houses labeled G are painted gray, how many of the seven remaining houses cannot be painted gray?

Without knowing what the figure looks like, I can’t say, but the process to follow to answer this is first to cross out all houses that can’t be gray given the rules. That means any house next to a G or across from a G gets crossed out.

To make sure you aren’t missing any, do each G one at a time: pick a house with a G in it, then cross off the house to the left, the house to the right, and the house across. Then move to the next G, etc. Since the question asks how many houses cannot be gray, count all the houses you crossed out, and that’s your answer.

One note: the current SAT doesn’t really ask questions like this. Are you sure you’re studying from up-to-date materials?

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