# SAT Math: Challenging Problems #9

Here we go again ….. five more problems in our series on Challenging SAT Math Problems. These problems cover geometry, algebra & functions, sequences, listing & counting, and statistics; this is a post with a little bit of everything!  Give them a try, and if you have any questions, be sure to let us know.  The solutions appear at the bottom of this post.

1)  ABCD is a rectangle.  Point X is the midpoint of side BC and Point Y is the midpoint of side DC .  If the area of pentagon ABXYD is 7/12, what is the area of the rectangle?

(A)  1/2
(B)  2/3
(C)  3/4
(D)  5/6
(E)  1

# SAT Math: Challenging Problems #8

Last week’s announcement from the College Board about the re-designed SAT has gotten a lot of attention.  It will be interesting to see what changes will be made to the Math section.  In the meantime, here are a few more challenging problems similar to those that would appear at the end of sections on the current version of the test.  Give them a try and, as usual, if you have a question feel free to drop us an email.  Solutions appear at the bottom of this post.

1)  In the diagram below, the yellow circle has an area of 9 pi and a center at Point A.  The green circle has an area of 25 pi and a center at Point B.  Both circles are tangent to the x-axis and the vertical line n.  If line m contains the origin as well as Points A and B, what are the coordinates of point A, the center of the yellow circle?

(A)  (3, 3)
(B)  (6, 3)
(C)  (8, 3)
(D)  (9, 3)
(E)  (12, 3)

# SAT Math: Challenging Problems #7

Here are five more challenging SAT math problems.  Give them a try and if you have any questions, leave a comment below or send us an email.  Answers appear at the bottom of this post.

1)            n = 3100 + 3104

The number n above has prime factors of 2 and 3.  What is the third prime factor of n?
(Note:  This is a “grid-in” problem.  You need to supply your own answer.)

2)  In the figure below, if n = 30, which of the following could be the coordinates of Point P?

(A)  $(6, 1)$
(B)  $(7, \sqrt{3})$
(C)  $(4\sqrt{3}, 1)$
(D)  $(8, 2)$
(E)  $(4+2\sqrt{3}, 4)$

# SAT Math: Challenging Problems #6

It’s been a while since we’ve done one of these posts.  Hopefully you’ll think these were worth the wait!  Give them a try and, as usual, if you have any questions, don’t hesitate to ask.  Answers appear at the bottom of this post.

1)  The circle below has its center at the origin and has an area of 25 pi.  The parabola has equation y = ax2 and intersects the circle at the points where x = 3 and x = -3.  What is the value of a?

(A)  4/9
(B)  5/9
(C)  3/5
(D)  4/5
(E)  4/3

# SAT Math: Challenging Problems #5

Here are five more problems in our series on challenging SAT Math questions.  Give them a try and see how you do.  As always, if you have a question about any of these, leave a comment below.  The answers to these problems are at the bottom of the post.

1)  Triangle AFE is both isosceles and right with the right angle at F.  Point C is both the midpoint of segment AE and the center of the circle.  If FE is 8 and AE = 2(BD), what is the area of the shaded region?

(A)  $32-2\pi$
(B)  $32-4\pi$
(C)  $32-8\pi$
(D)  $64-4\pi$
(E)  $64-8\pi$