Question

The roman numeral for the greatest two-digit number is:
A) IC
B) LIL
C) ICCCCD
D) XCIX

Answer 1

Hint: The Roman numeral system is a number system that has seven symbols to represent the numbers. The seven symbols are I, V, X, L, C, D, and M. Each symbol has a separate value.
$\text{I}=1$, $\text{V}=5$, $\text{X}=10$, $\text{L}=50$, $\text{C}=100$, $\text{D}=500$ and $\text{M}=1000$.
To form the numerical values in this system, we place the symbols side by side to denote the arithmetic operation.

Complete step by step solution:
In the Roman numeral system, the symbols are written side by side to denote the arithmetic operation on the nearby symbol.
We shall start from right to left. If the symbol on the left side is greater than or equal to the symbol on the right, we add their values. And if the symbol on the left side is lower than that on the right, we subtract them.
$\Rightarrow 4=\text{IV }\left( 5-1 \right)$
$\Rightarrow 6=\text{VI }\left( 1+5 \right)$
We cannot add more than three numerals in a row. Also, we cannot subtract more than two numerals in a row. Therefore, $\text{IIII}=4$ and $\text{IIIV}=2$ are wrong.
A numeral that can be subtracted from a larger numeral should be ${{{}^{1}/{}_{5}}^{th}}$ or ${{{}^{1}/{}_{10}}^{th}}$ of the larger one.
For example, we cannot subtract I from L but we can subtract I from X.
Using these phenomena, let us find out which given option is equal to 99.
Option A): IC
This one is equal to 99 because $\left( \text{C}=100 \right)$ and $\left( \text{I}=1 \right)$.
$\Rightarrow \text{IC}=100-1=99$
But I is ${{{}^{1}/{}_{100}}^{th}}$ of the C and not ${{{}^{1}/{}_{10}}^{th}}$. It violates a general rule we saw earlier. Therefore this is a wrong representation of the number 99.
Option B): LIL
This one is also equal to 99, but it is not a valid Roman numeral.
$\Rightarrow \text{LIL}=\text{50-1+50}=\text{99}$
Because the numeral I, which is subtracted from L is actually ${{{}^{1}/{}_{50}}^{th}}$ of L. Therefore this representation is also wrong.
Option C): ICCCCD
This option is also equal to 99 but it is a wrong representation. Let us see why.
$\Rightarrow \text{ICCCCD}=500-100-100-100-100-1=99$
We cannot subtract more than two numerals in a row.
Option D): XCIX
$\Rightarrow \text{XCIX}=10-1+100-10=99$
Here we have subtracted I from X and X from C. The numeral I is ${{{}^{1}/{}_{10}}^{th}}$ of X and the X is ${{{}^{1}/{}_{10}}^{th}}$ of C.

Therefore, the roman numeral equal to the greatest two-digit number is XCIX.

Note:
The important rules of thumb we should consider while converting a Roman numeral into an Arabic numeral are as follows.
The numeral on the right side gets added and the numeral on the left side gets subtracted. We cannot add more than three numerals in a row and we cannot subtract more than two numerals in a row. A numeral that can be subtracted from a larger numeral should be ${{{}^{1}/{}_{5}}^{th}}$ or ${{{}^{1}/{}_{10}}^{th}}$ of the larger one.