4.3 Sample Questions
PS19062
- Two numbers differ by 2 and sum to S. Which of the
following is the greater of the numbers in terms of S?
(A) —s - 1
2
(B)
s
2
(C) s
-+-^1
2 2
(D)
—s + 1
2
(El
—s + 2
2
｀
PS00904
- The figure shown above consists of three identical
circles that are tangent to each other. If the area of the
shaded region is 64/3 - 32冗，what is the radius of
each circle?
4
8
16
24
32
因佃＠回旧
PS02053
135.In a numerical table with 10 rows and 10 columns ,
each entry is either a 9 or a 10. If the number of 9s in
the nth row is n -l for each n from 1 to 10 , what is
the average (arithmetic mean) of all the numbers in the
table?
(A) 9. 45
(B) 9. 50
(C) 9. 55
(D) 9. 65
(E) 9. 70
PS08485
- A positive integer n is a perfect number provided that
the sum of all the positive factors of n, including 1 and
n, is equal to 2n. What is the sum of the reciprocals of
all the positive factors of the perfect number 28?
(Al
l-4
(B)
56
27
(C) 2
(D) 3
(El^4
PS11430
- The infinite sequence a 1 , a 2 , ... , an, ... is such that
a 1 = 2, a 2 = -3, a 3 = 5, a4 = -1, and an= an _ 4 for n > 4.
What is the sum of the first 97 terms of the sequence?
(A) 72
(Bl^74
(C)^75
(D)^78
(E)^80
PS09901
138. The sequence a 1 , a 2 , ... an, ... is such that
an = 2an _ 1 - x for all positive integers n ::::: 2 a叩伽a
certain number x. If a 5 = 99 and a3 = 27 , what is the
value of x?
(A)^3
(B)^9
(C)^18
(D)^36
(El^45
PS03779
- A window is in the shape of a regular hexagon with each
side of length 80 centimeters. If a diagonal through the
center of the hexagon is w centimeters long , then w =
(Al 80
(Bl^120
(Cl^150
(D)^160
(El^240
