one that has the point (0,−500) on it.
25 . E Expand out the 6! and the 5! in the original expression to get .
Cancel out all the numbers in the denominator, and you’re left with 6 × 4!. Since the problem
tells you that 4! = 24, multiply 6 by 24: 6 × 24 = 144.
26 . G Try PITA for this one. Since they’re in order, start with (H). If Alfred buys 56 stamps for
$0.45 each, he spends 56 × $0.45 = $25.20 on the more expensive stamps. Since the total he
spends on all stamps is $25, (H) is too large, and you can also eliminate (J) and (K). Try
(G): if Alfred buys 48 stamps for $0.45 each, he spends 48 × $0.45 = $21.60 on the more
expensive stamps. Because he bought 65 stamps total, subtract the number of $0.45 stamps to
find the number of $0.20 stamps: 65 − 48 = 17. Multiply 17 by $0.20 to find the amount
Alfred spent on the less expensive stamps: 17 × $0.20 = $3.40. Add the amount he spend on
the more expensive stamps to the amount he spent on the less expensive stamps: $21.60 +
$3.40 = $25. This total matches what you’re given in the problem, so (G) is correct.
27 . E To find the area of the shaded region, find the area of the larger figure and subtract the area of
the smaller figure. If the square has a side of length 2, its area is A = s^2 = 2^2 = 4. To find the
area of the circle, draw a diagonal in the square, which is also the diameter of the circle.
Dividing the square in half diagonally gives you two 45-45-90 triangles. Since the ratio of
sides of a 45-45-90 triangle is x:x:x and here x = 2, the length of the diagonal is 2 . The
radius of the circle is half the diameter, so divide the length of the diagonal by 2 to find the
radius: 2 ÷ 2 = . The area of the circle is A = πr^2 = π( )^2 = 2π. Subtract the area of
the square from the area of the circle to find the area of the shaded region, 2π −4.
28 . H Set up a proportion using the ratio given for the triangles, and the one side length given,
, then solve for x. Cross multiply to get 36 = 4x, then divide both sides by 4 to get x =
9. Choice (K) sets up the proportion as , which incorrectly matches the length of 12
to the smaller triangle in the proportion.
29 . B Start by finding the measure of VZW. Since WZY and VZW make a straight line, VZW
= 180° − 145° = 35°. As figure WXYZ is a parallelogram, you know the measure of WZ is
equal to 10, the length of XY. You can now solve for VZ. Use this information to find out that
cos 35° = , and so cos 35° = . Multiply both sides by 10 to find that VZ =
