SAT Question of the Day Explained – October 13, 2014 – Math

Today’s SAT Question of the day is a quick and easy math problem.  The test makers would like to know how many non-overlapping squares with side length 3 can fit inside a square with side length 6.  My favorite way to solve this is with some quick sketches:

squares-1

Once we have our two model squares, we can see how they would relate.  Since 3 x 2 = 6, we know we can fit two small squares across the bottom of the big square.  However, there is still some room left over on top!  That room is the exact size of two more small squares, leaving us with the following:

squares-2

Four small squares inside the larger square.  Quick check: 6 x 6 (area of the large square) = 36. 3 x 3 = 9 (area of the small square); four small squares means that we have 4 x 9 = 36 units of area inside the small squares as well.  Success!