SAT Math: Challenging Problems #6

It’s been a while since we’ve done one of these posts.  Hopefully you’ll think these were worth the wait!  Give them a try and, as usual, if you have any questions, don’t hesitate to ask.  Answers appear at the bottom of this post.

1)  The circle below has its center at the origin and has an area of 25 pi.  The parabola has equation y = ax2 and intersects the circle at the points where x = 3 and x = -3.  What is the value of a?

Challenge 6-1

(A)  4/9
(B)  5/9
(C)  3/5
(D)  4/5
(E)  4/3

2)  Both of the adjacent squares below have one side on the x-axis.  The smaller square has an area of 16 square units and one of its vertices is Point X.  The larger square has an area of 25 square units and one of its vertices is Point Y.  Line m contains both Points X and Y and also passes through the origin.  What other point must be on line m?

Challenge 6-2

(A)  (9, 3)
(B)  (12, 8)
(C)  (15, 4)
(D)  (20, 6)
(E)   (35, 7)

3)                       8, 64, 512, 4096, ……..

Each term after the first term in the geometric sequence above is found by multiplying the preceding term by 8.  What will be the units (ones) digit of the 125th term? 

(A)  1
(B)  2
(C)  4
(D)  6
(E)   8

4)  Let’s define a three-digit number as “even-odd-even” if the first digit is even, the second odd and the third even.  Similarly, let’s define such a number as “odd-even-odd” if the first digit is odd, the second even and the third odd.  How many three-digit positive integers are either “even-odd-even” or “odd-even-odd”?

(A)  100
(B)  225
(C)  250
(D)  333
(E)  500

5)   The cube below has edges that are each x inches long.  If CB = 2DC, what is the length (in inches) of the segment connecting the vertex A to Point C?

Challenge 6-5

 

(A)   \frac{\sqrt{22} }{3} x
(B)   3 \sqrt{3} x
(C)   \frac{2 \sqrt{3} }{4} x
(D)   \frac{8}{3} x
(E)   \frac{15}{2} x

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)  (A)
2)  (E)
3)  (E)
4)  (B)
5)  (A)

 

 

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