MathDB
Problems
Contests
National and Regional Contests
USA Contests
MAA AMC
AMC 12/AHSME
2001 AMC 12/AHSME
2
2
Part of
2001 AMC 12/AHSME
Problems
(1)
P(n) and S(n)
Source:
12/3/2005
Let
P
(
n
)
P(n)
P
(
n
)
and
S
(
n
)
S(n)
S
(
n
)
denote the product and the sum, respectively, of the digits of the integer
n
n
n
. For example, P(23) \equal{} 6 and S(23) \equal{} 5. Suppose
N
N
N
is a two-digit number such that N \equal{} P(N) \plus{} S(N). What is the units digit of
N
N
N
?
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
a
n
>
2
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
a
n
>
3
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
a
n
>
6
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
a
n
>
8
<
s
p
a
n
c
l
a
s
s
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
a
n
>
9
<span class='latex-bold'>(A)</span> \ 2 \qquad <span class='latex-bold'>(B)</span> \ 3 \qquad <span class='latex-bold'>(C)</span> \ 6 \qquad <span class='latex-bold'>(D)</span> \ 8 \qquad <span class='latex-bold'>(E)</span> \ 9
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
A
)
<
/
s
p
an
>
2
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
B
)
<
/
s
p
an
>
3
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
C
)
<
/
s
p
an
>
6
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
D
)
<
/
s
p
an
>
8
<
s
p
an
c
l
a
ss
=
′
l
a
t
e
x
−
b
o
l
d
′
>
(
E
)
<
/
s
p
an
>
9
MATHCOUNTS