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* = 3^{100} + 3^{104}

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)

(B)

(C)

(D)

(E)

3) If 0 < *x* < *y* and (2*x* + *y*)^{2} – (2*x* – *y*)^{2} < 2, what is the greatest possible value of *x*?

(A) ¼

(B) ½

(C) 1

(D) 2

(E) 4

4) A game involves placing the following cards face down in a row:

The cards are turned over and you win if NEITHER the grey shaded card NOR the red shaded card appears in the first, second or third positions in the row. How many different arrangements of cards result in you winning?

(A) 6

(B) 12

(C) 24

(D) 72

(E) 120

5) Let the function *f* be defined by *f*(*x*) = *x*^{2} + 4*x* – 7. Which of the following could be true for some non-negative value of *x*? (Note: To say that *x* is non-negative is the same as saying *x* > 0)

I. *f*(*x*) = *f*(*x* – 1)

II. *f*(*x*) = *f*(*x* – 5)

III. *f*(*x *+ 2) = *f*(*x* – 6)

(A) I only

(B) II only

(C) III only

(D) II and III only

(E) I, II and III

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) 41

2) (B)

3) (B)

4) (B)

5) (D)