AoPS Community
2001 AMC 10
AMC 10 2001
by #H34N1, Silverfalcon, mysmartmouth, worthawholebean, rrusczyk
1
The median of the list
n, n
+ 3
, n
+ 4
, n
+ 5
, n
+ 6
, n
+ 8
, n
+ 10
, n
+ 12
, n
+ 15
is
10
. What is the mean?
(A)
4
(B)
6
(C)
7
(D)
10
(E)
11
2
A number
x
is
2
more than the product of its reciprocal and its additive inverse. In which interval
does the number lie?
(A)

4
≤
x
≤ 
2
(B)

2
< x
≤
0
(C)
0
< x
≤
2
(D)
2
< x
≤
4
(E)
4
< x
≤
6
3
The sum of two numbers is
S
. Suppose 3 is added to each number and then each of the re
sulting numbers is doubled. What is the sum of the final two numbers?
(A)
2
S
+ 3
(B)
3
S
+ 2
(C)
3
S
+ 6
(D)
2
S
+ 6
(E)
2
S
+ 12
4
What is the maximum number of possible points of intersection of a circle and a triangle?
(A)
2
(B)
3
(C)
4
(D)
5
(E)
6
5
How many of the twelve pentominoes pictured below have at least one line of symmetry?
(A)
3
(B)
4
(C)
5
(D)
6
(E)
7
6
Let
P
(
n
)
and
S
(
n
)
denote the product and the sum, respectively, of the digits of the integer
n
. For example,
P
(23) = 6
and
S
(23) = 5
. Suppose
N
is a twodigit number such that
N
=
©
2019 AoPS Incorporated
1
AoPS Community
2001 AMC 10
P
(
N
) +
S
(
N
)
. What is the units digit of
N
?
(A)
2
(B)
3
(C)
6
(D)
8
(E)
9
7
When the decimal point of a certain positive decimal number is moved four places to the right,
the new number is four times the reciprocal of the original number. What is the original num
ber?
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 Spring '20
 Numerical digit, Decimal, AoPS Incorporated