broccoli fractal (source)

Pattern questions on the SAT aren’t super common, but they tend to give people all sorts of difficulty when they do appear. Let’s take one apart.

  1. A farmer is planting a row of plants. He first plants 2 broccoli plants, then 3 cabbage plants, then 1 apple tree, then 2 orange trees, then 1 dill weed plant. He repeats this pattern over and over again until he’s filled up all the land on his (very unorthodox) farm. What kind of plant is the 782nd one he plants?
    (A) cabbage
    (B) apple
    (C) broccoli
    (D) dill weed
    (E) orange

Obviously I’m taking some liberties with the writing style of the test makers, but take away the goofiness and this question could totally appear on your SAT. How do you solve it?

Start by writing a few iterations of the pattern on top of each other:

B, B, C, C, C, A, O, O, M,
B, B, C, C, C, A, O, O, M,
B, B, C, C, C, A, O, O, M, …

Now number the ends of the lines (in green here):

(1)B, B, C, C, C, A, O, O, M (9),

(10)B, B, C, C, C, A, O, O, M (18),

(18)B, B, C, C, C, A, O, O, M(27), …

Note that down the RIGHT side of your lines you’re basically counting up by multiples of 9. On the LEFT side, you’re also counting up by 9’s, but in a slightly more confusing way. The mistake a lot of people make on pattern questions is that they start counting from the beginning of the pattern, and they get all screwed up. Count from the end of the pattern to make this easy on yourself!

Every even multiple of 9 will be a dill weed plant. We want the 782nd plant. 782 ÷ 9 = 86 remainder 8, which means the 782nd plant will be the 8th in our pattern. In other words, it’ll be an orange tree. (E) is our answer. Another way to think of this: the 783rd plant will be a dill weed plant, so the 782nd will be an orange tree.

No sweat, right? Sit down, SAT. You can’t slow me down with that weak sauce.

Of course, repeating patterns like the one above are only one kind of pattern that might get thrown at you, just the kind that seem to give students the most trouble, in my experience. The drill below contains more pattern-type questions.

Try these examples:

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