discount per purse, which turns out to be $5.50. Now add that to the sale price of a single
purse, and you get $17.50 as the non-discount price.
9 . A You can Plug In, though the numbers will get fairly large once you start taking things to the 4th
power. Or you can solve it as a quadratic, using FOIL. You may recognize it as a twist on (x
+ y)(x − y). You know that when one binomial is a sum and the other a difference, their
product will be the difference of two squares, so eliminate (C). After that, just make sure
everything gets squared, coefficients as well as variables, and you wind up with (A).
10 . H The formula for a rectangle’s area is base × height. PITA to find which answer choice fits the
parameters in the question. Remember to start with the middle value! If we use 6 for the
longer side of the rectangle, that means the short side will be 3 because we need an area of
18. Adding all four sides together gives us 6 + 6 + 3 + 3 = 18, the perimeter given in the
question, so (H) is the correct answer.
11 . C The sum of all the angles in any triangle is 180. Since X is 64°, the sum of Y and Z is
calculated by subtracting 64° from 180°, leaving 116°.
12 . K Every possibility must be accounted for. For each of the four skirts, there are five sock
options. 4 × 5 = 20, so there are 20 skirt/sock combinations. For each of those 20
combinations, there are three sweater options: 20 × 3 = 60, so there are 60
skirt/sock/sweater combinations. Finally, for each of these 60 combinations, there are 4
headband options: 60 × 4 = 240 total outfit combinations.
13 . D Use PITA. Start with the middle answer, (C), and you’ll get 14 + 2(15) + = 52, so you
know you need a higher set of numbers. Go to (D), and you’ll get 16 + 2 (17) + = 59.
14 . J When ACT gives you a function and then identifies a number inside the parentheses, it means
to plug that number in for x every time it appears in the question. In this case, x = −2, so the
function will end up reading h(x) = −5(−2)^3 . Then you get h(x) = −5(−2)^3 . (−2)^3 = −8, and
when you multiply that by −5, you get 40. Watch out for the traps in (F) and (K), which
involve cubing the −5 along with the x.
15 . B Don’t overcomplicate here. Grab your calculator to see what the 4th root of 97 is (it’s in the
“Math” menu of your graphing calculator). Another approach would be to recognize that z =
could be altered to read z^4 = 97. This way, you can PITA. Since 3^4 = 81, and 4^4 = 256,
the value of z must be between 3 and 4.
16 . F The simplest approach is to PITA. Grab your calculator and divide each of the numbers in the
