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MAA AMC
AMC 12/AHSME
1982 AMC 12/AHSME
15
Greatest Integer Function
Greatest Integer Function
Source:
January 16, 2006
function
floor function
Problem Statement
Let
[
z
]
[z]
[
z
]
denote the greatest integer not exceeding
z
z
z
. Let
x
x
x
and
y
y
y
satisfy the simultaneous equations
y
=
2
[
x
]
+
3
,
y
=
3
[
x
−
2
]
+
5.
\begin{array}{c} y=2[x]+3, \\ y=3[x-2]+5. \end{array}
y
=
2
[
x
]
+
3
,
y
=
3
[
x
−
2
]
+
5.
If
x
x
x
is not an integer, then
x
+
y
x+y
x
+
y
is
(A)
an integer
(B)
between 4 and 5
(C)
between -4 and 4
(D)
between 15 and 16
(E)
16.5
\textbf {(A) } \text{an integer} \qquad \textbf {(B) } \text{between 4 and 5} \qquad \textbf {(C) } \text{between -4 and 4} \qquad \textbf {(D) } \text{between 15 and 16} \qquad \textbf {(E) } 16.5
(A)
an integer
(B)
between 4 and 5
(C)
between -4 and 4
(D)
between 15 and 16
(E)
16.5
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