turkey-yks 2016 Q6

turkey-yks · Other · lys1-math Number Theory Combinatorial Number Theory and Counting
In the following table consisting of 100 unit squares numbered from 1 to 100, some squares will be painted.
123$\ldots$10
111213$\ldots$20
....
....
....
919293..100

Squares with even numbers are painted yellow, squares that are multiples of 3 are painted red, and squares that are multiples of 5 are painted blue.
For a square to be orange, it must be painted only yellow and red.
Accordingly, how many unit squares in the table are orange?
A) 8
B) 12
C) 13
D) 15
E) 18 
In the following table consisting of 100 unit squares numbered from 1 to 100, some squares will be painted.

\begin{center}
\begin{tabular}{ | c | c | c | c | c | }
\hline
1 & 2 & 3 & $\ldots$ & 10 \\
\hline
11 & 12 & 13 & $\ldots$ & 20 \\
\hline
. & . & . &  & . \\
. & . & . &  & . \\
. & . & . &  & . \\
\hline
91 & 92 & 93 & .. & 100 \\
\hline
\end{tabular}
\end{center}

Squares with even numbers are painted yellow, squares that are multiples of 3 are painted red, and squares that are multiples of 5 are painted blue.

For a square to be orange, it must be painted only yellow and red.

Accordingly, how many unit squares in the table are orange?\\
A) 8\\
B) 12\\
C) 13\\
D) 15\\
E) 18
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