SAT Math: Challenging Problems #9

Here we go again ….. five more problems in our series on Challenging SAT Math Problems. These problems cover geometry, algebra & functions, sequences, listing & counting, and statistics; this is a post with a little bit of everything!  Give them a try, and if you have any questions, be sure to let us know.  The solutions appear at the bottom of this post.

1)  ABCD is a rectangle.  Point X is the midpoint of side BC and Point Y is the midpoint of side DC .  If the area of pentagon ABXYD is 7/12, what is the area of the rectangle?

Challenge 9-1

(A)  1/2
(B)  2/3
(C)  3/4
(D)  5/6
(E)  1

2)  The parabola has an equation in the form y = ax2 + b.  If the rectangle has an area of 126 square units, what is the value of ab?

Challenge 9-2

(A)  3
(B)  4
(C)  6
(D)  9
(E)  12

3)      20, – 10, 5, -2.5, …….

In the geometric sequence above, how many of the first 50 terms are less than one?

(A)  21
(B)  22
(C)  25
(D)  46
(E)  47

4)  At a carnival, four prizes were distributed between Aaron, Ben and Candice.  There was no guarantee that each of them would get a prize (in other words, one or more of them could have gotten no prize at all).  If Aaron got at least one prize, in how many ways could the prizes have been distributed?

(A)  6
(B)  8
(C)  10
(D)  12
(E)  24

5)  In a kindergarten class, the teacher surveys the class about how many pets they have.  The results of the survey are:

Challenge 9-5

A new student moves in.  When her results are added to the survey, the average (arithmetic mean) number of pets is equal to exactly twice the median number of pets.  How many pets does the new student have?

(A)  0
(B)  1
(C)  2
(D)  3
(E)  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)  (C)
3)  (E)
4)  (C)
5)  (D)

 

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