Question

Assertion: The value of \[CM - CD + CVII\] is 607.
Reason: Symbol C can be added to every Roman symbol, but it can be subtracted from D and M only.
A) Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B) Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
C) Assertion is correct but Reason is incorrect
D) Assertion is incorrect but Reason is correct

Answer 1

Hint: Roman numerals are the letters used by the ancient Romans to represent numbers. As the given value of \[CM - CD + CVII\] is 607, we need to convert the Roman value to Decimal value to get the value as 607. Hence, to find the correct statements of Assertion and Reason we can easily find after converting it to decimal with respect to the roman value given in the reason statement.

Complete step-by-step solution:
Let us write the given statement:
The value of \[CM - CD + CVII\] is 607.
We need to convert the roman numerals to decimal value as:
\[CM - CD + CVII = 900 - 400 + 107 = 607\]
Hence, Statement 1 is true and Statement 2 is also true.

Therefore, option A is the correct answer.

Additional information: Roman numerals are the numbers that were used in ancient Rome, which employed combinations of letters from the Latin alphabet.

Note: We must note that the Roman numerals use a numbering technique based on seven letters: I, V, X, L, C, D and M. The symbol I represents a value of 1; V represents 5; X represents 10; L represents 50; C represents 100; D represents 500 and M represents 1000. Thus, the key point to solve this question is that we must know all the roman numerals of the number system.