# SAT Math: Challenging Problems #3

Here’s another set of five challenging SAT Math problems.  Give them a try and see what you think.  Answers are at the bottom of the page.  Good luck!

1)  A recent athletic department meeting was held only for students who play football, lacrosse or both.  Of those in attendance, 1/5 of the football players also play lacrosse, and 1/3 of the lacrosse players also play football.  Which of the following could be the number of students who attended the meeting?

(A)  25
(B)  28
(C)  30
(D)  54
(E)  80

2)  An equilateral triangle is inscribed in a circle with an area of 16 pi.  What is the area of the triangle?

(A) $8$
(B) $6\sqrt{3}$
(C) $8\sqrt{3}$
(D) $12\sqrt{3}$
(E) $24\sqrt{3}$

3)  The function f(x) is defined by the equation f(x) = ax2 + 12.  Point A is the vertex of the parabola and Points B and C are the x-intercepts.  If the area of Triangle ABC is 72 square units, what is the value of a?

(A)  -1/2
(B)  -1/3
(C)  -1/4
(D)  -1/6
(E)  -1/12

4)  in the figure below, BC = 20, AE = 15 and BD = 12.  What is the length of segment AC?

Note:  Figure Not Drawn to Scale

(A)  18
(B)  22
(C)  23
(D)  25
(E)  30

5)  Let M be equal to the square of the positive integer m.  If m is greater than 2, which of the following is equal to the square of the integer 2 less than m?

(A)  $\sqrt{M-2}$
(B)  $M-2$
(C)  $M-4\sqrt{M}+4$
(D)  $M-4$
(E)  $M^{2}-4$

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 info@cardinalec.com .

Solutions:
1)  (B)
2)  (D)
3)  (B)
4)  (D)
5)  (C)