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)

2)  In a certain class, there are n girls.  The number of boys in the class is ten fewer than three times the number of girls.  Which of the following is an expression for the percent of girls in the class?

(A)   $\frac{n}{3n-10}$ %
(B)   $\frac{n}{4n-10}$ %
(C)   $\frac{100n}{3n-10}$ %
(D)   $\frac{100n}{4n-10}$ %
(E)    $\frac{3n-10}{4n-10}$ %

3)          3x –   y + 4z = 11
2x + 3y –   z =    9
x – 2y – 3z =   4

In the system of equations above, what is the value of x?

(A)  3
(B)  4
(C)  5
(D)  6
(E)  7

4)  How many three digit numbers are there in which all three digits are unique (in other words, no digit repeats)?  For example, 323 would NOT be such a number because the 3 is repeated.

(A)  504
(B)  612
(C)  648
(D)  720
(E)  900

5)  The three congruent circles below, with centers at Points A, B and C, are tangent to both the  x-axis and y-axis as shown.  What is the area of the yellow shaded region?

(A)  $2- \pi$
(B)  $2-\frac{\pi }{2}$
(C)  $2-\frac{\pi }{4}$
(D)  $4- \pi$
(E)  $4-\frac{\pi }{2}$

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)  (D)
3)  (B)
4)  (C)
5)  (B)