Question

Which of the Roman Numerals are correctly written
a) VC
b) IL
c) DV
d) XXIV
e) VVII
f) XII

Answer 1

Hint: We start solving this problem by first discussing the restriction of subtraction of the roman numerals. Then we consider the numerals given in each subpart of the question and convert them into numbers and see if the conversion is correct according to the discussed restriction and find if the given numerals are correct or wrong.

Complete step by step answer:
First, let us discuss a restriction in the roman numerals.
When it comes to subtracting in the roman numerals, only powers of 10 are subtracted, like I, X, or C, but not V or L and only from the next two higher digits in the order {I, V, X, L, C, D}.

a) VC
The numeral VC indicates that the number V subtracted from the number C, which is the number 5 subtracted from the number 100.
But according to the above discussed restriction, we cannot subtract V from C. So, the given numeral is wrong.

b) IL
The numeral I indicates the number 1.
The numeral L indicates the number 50.
So, from the above discussed property of subtraction, we cannot subtract I from L as it is not in the immediate two digits after I.
Hence, the given numeral IL is not correct.

c) DV
The numeral D indicates 500.
The numeral V indicates 5.
So, now we need to add 5 to 500. As there is no restriction for the addition of the roman numerals, we can add them directly. Then, we get,
DV=500+5=505.
Hence the given roman numeral is correct.

d) XXIV
As the numerals IV are to the right side of XX, we need to add IV to XX.
As X indicates 10, then XX indicates 20. The numeral IV indicates the number 4. Now, let us add them. Then we get,
XXIV=20+4=24
Hence, the given numeral is correct.

e) VVII
The numeral V indicates the number 5 and the numeral I indicates the number 1.
Then we get,
VVII=5+5+1+1=12
But we can write the number 12 in the roman numeral as XII, which is a simplified form.
Hence, the given numeral is wrong.

f) XII
The numeral X indicates the number 10 and the numeral I indicates 1.
Then we get
XII=10+1+1=12
Hence the given numeral is correct.

Note:
 The common mistake one makes while solving this problem is one might use the same restriction that we have used for the subtraction of the roman numerals also for the addition of Roman numerals and mark most of the answers as wrong. But we need to remember that the restriction applies only to the subtraction of the roman numerals.