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?

Challenge 5-1

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

2)  Sam drives 20 miles due east, then 12 miles due north.  After a brief stop for lunch, he drives 6 miles due west and then 2 miles due south.  How many miles is Sam away from his starting point?

(A)  4\sqrt{15}
(B)  20
(C)  2\sqrt{74}
(D)  24
(E)  40

3)  Line m contains the points (1, 17) and  (3, 11).  Line n is perpendicular to line m and passes through the origin.  One point on line n is (b, b – 8).  What is the value of b?

(A)  2
(B)  4
(C)  6
(D)  8
(E)  12

4)  If 2a + b = k, what is the value of 22a + 2b + 3 in terms of k?

(A)  3k
(B)  6k
(C)  8k
(D)  6k2
(E)  8k2

5)  There are four senior counselors at a camp, each of whom is involved in training the three junior counselors.  Each training session involves one senior counselor and either one, two or all three of the junior counselors. How many different groups of people could be involved in any given training session?

(A)  12
(B)  20
(C)  24
(D)  28
(E)  40

If you have questions about these problems or anything else to do with the SAT, leave a comment below or send me an email at .


1)  (B)
2)  (C)
3)  (E)
4)  (E)
5)  (D)

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