2.6 SAT Math - Patterns

SAT Pattern Example Question:

A commemorative quilt is being sewn in the repeating pattern heart, cross, circle, star, crescent.  If the quilter's first quilt square has the shape of a star, what shape appears on the 73rd square?

(A) heart
(B) cross
(C) circle
(D) star
(E) crescent

These questions look intimidating simply because it feels like you're going to have to write it all out, as if your work is going to look like:

star, crescent, heart, cross, circle, star, crescent, heart, cross, circle...

And on and on until you get to number 73.  You can do it this way; it just takes a really long time and is unnecessary if you remember this simple hint:

-Hint: SAT Pattern problems are usually remainder problems in disguise.

Answer

What's the question above really asking? When 73 (the number of thing they're asking about) is divided by 5 (the number of objects in the pattern), what is the remainder? Then count that many in your shape group, starting with the one they told you to start with, and answer that. 

So in this case, 73÷5=14.6, but we do our remainder trick on the calculator to determine the whole number remainder is 3, and then we count 3, starting from the star: star, crescent, heart.  The answer is (A) heart.

-Trick to Watch Out For: If you get a remainder of zero, you are at the end of the pattern.  So if they had asked, in that same example, what shape was on the 75th square, the answer would have been circle, since 5 goes into 75 evenly, and the pattern began with star.