Question

The number of matchsticks that can be used to write 23 in Roman system are,
A. 6
B. 7
C. 8
D. 9

Answer 1

Hint: For the above question we will have to write 23 in Roman system by using the Roman numerals which are represented by following letters:
$\begin{align}
  & I-1 \\
 & V-5 \\
 & X-10 \\
 & L-50 \\
 & C-100 \\
 & D-500 \\
 & M-1000 \\
\end{align}$
By using the above if a numeral is followed by another numeral of lower denomination, then the two will be added if it is preceded by one of lower denomination then the smaller numeral is subtracted from the greater.

Complete step-by-step answer:

We have been asked to find the number of matchsticks that can be used to write 23 in Roman system.
We know that Roman numerals are as follows,
$\begin{align}
  & I-1 \\
 & V-5 \\
 & X-10 \\
 & L-50 \\
 & C-100 \\
 & D-500 \\
 & M-1000 \\
\end{align}$
So, we will use this to write 23 in Roman system.
In Roman system 23 $=XXIII$
We can also verify, if a numeral is followed by another numeral of lower denomination. Then the two will be added if it is preceded by one of lower denomination the smaller numeral is subtracted from greater.
$\Rightarrow XXIII=10+10+1+1+1=23$
Now, we have to count the number of matchsticks that will be used to write $XXIII$.
For X, we need 2 matchsticks and for I we need 1 matchstick. So, clearly, we can see the number of matchsticks is equal to $2+2+1+1+1=7$.
Therefore, the correct option is B.

Note: Be careful while writing the number 23 in Roman system as it might be possible that you write 23 as $XXXVII$ and you treat it like $\left( 10+10+10-7 \right)$ which is absolutely wrong and not according to the Roman system.