2001 AMC 10
AMC 10 2001
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 resulting 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
Contributors: #H34N1, Silverfalcon, mysmartmouth, worthawholebean, rrusczyk

2001 AMC 10
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
two-digit number such that
N
=
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 number?
(A)
0
.
0002
(B)
0
.
002
(C)
0
.
02
(D)
0
.
2
(E)
2
8
Wanda, Darren, Beatrice, and Chi are tutors in the school math lab.
Their
schedule is as follows: Darren works every third school day, Wanda works every

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- Fall '19
- Numerical digit, Decimal, c Mathematical Association of America