# SAT Math: Challenging Problems #10

It’s been a while since we’ve updated our series of SAT Math Challenge Problems (you can see all of the problems here).  Here are five more problems designed to resemble those you’d find at the end of an SAT Math section.  Give your brain a workout and let us know what you think.  The solutions appear at the bottom of this post.

1)  Let the functions f and g be defined completely by the table below.  If f(a) < a for some number a, what is the value of g(a)? (A)  -6
(B)  -4
(C)  -2
(D)   3
(E)   5

2)  If (x + 3) is a factor of 3x2 + 5x + k, where k is some integer, what is the value of k?

(A)  -12
(B)  -6
(C)  -4
(D)  6
(E)   12

3)  If ⇑x is defined by  ⇑x = $\frac{x-1}{x+4}$ for all values of x ≠ -4, which of the following is equivalent to 2 + ⇑x ?

(A) $\frac{x+1}{x+4}$
(B) $\frac{2x-2}{x+4}$
(C) $\frac{x-1}{x+6}$
(D) $\frac{3x+7}{x+4}$
(E) $\frac{3x+9}{x+4}$

4)  In an arithmetic sequence, the first term is x.  After the first term, each term is found by adding four to one-half the preceding term.  What is the ratio of the third term to the second term?

(A) $\frac{x}{2}$
(B) $\frac{x+6}{2x+4}$
(C) $\frac{x+4}{2x+6}$
(D) $\frac{x+24}{2x+16}$
(E) $\frac{x+8}{4x+6}$

5)  You are able to ride your bicycle to your friend’s house at an average rate of 15 miles per hour.  On the return trip along the same route, you ride at an average rate of 10 miles per hour.  What is your average rate, in miles per hour, for the round trip?

(A)  11
(B)  11.5
(C)  12
(D)  12.5
(E)   13

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)  E
(2)  A
(3)  D
(4)  D
(5)  C