csat-suneung 2005 Q11

csat-suneung · South-Korea · csat__math-humanities 4 marks Number Theory Combinatorial Number Theory and Counting
As shown in the figure below, for a natural number $n$, $n$ terms $$\left[ \frac { n } { 1 } \right] \left[ \frac { n } { 2 } \right] \left[ \frac { n } { 3 } \right] , \cdots , \left[ \frac { n } { n } \right]$$ are arranged in the $n$-th row from column 1 to column $n$ in order. (Here, $[ x ]$ is the greatest integer not exceeding $x$.)
Select all correct statements from . [4 points]
ㄱ. In row $n$, the number of terms with value 1 is $\left[ \frac { n + 1 } { 2 } \right]$. ㄴ. In row 100, the number of terms with value 3 is 8. ㄷ. In column 3, the number of terms with value 5 is 5.
(1) ㄱ
(2) ㄴ
(3) ㄷ
(4) ㄱ, ㄴ
(5) ㄱ, ㄴ, ㄷ
As shown in the figure below, for a natural number $n$, $n$ terms
$$\left[ \frac { n } { 1 } \right] \left[ \frac { n } { 2 } \right] \left[ \frac { n } { 3 } \right] , \cdots , \left[ \frac { n } { n } \right]$$
are arranged in the $n$-th row from column 1 to column $n$ in order.\\
(Here, $[ x ]$ is the greatest integer not exceeding $x$.)

Select all correct statements from <Remarks>. [4 points]

<Remarks>\\
ㄱ. In row $n$, the number of terms with value 1 is $\left[ \frac { n + 1 } { 2 } \right]$.\\
ㄴ. In row 100, the number of terms with value 3 is 8.\\
ㄷ. In column 3, the number of terms with value 5 is 5.\\
(1) ㄱ\\
(2) ㄴ\\
(3) ㄷ\\
(4) ㄱ, ㄴ\\
(5) ㄱ, ㄴ, ㄷ