Test: Roman Numerals- 2 - Class 4 MCQ

- The Roman numeration system uses basic numerals to represent numbers.
- There are 7 basic Roman numerals:
- I for 1
- V for 5
- X for 10
- L for 50
- C for 100
- D for 500
- M for 1000
- These numerals can be combined to form other numbers.
- Thus, the correct answer is D: 7.

- Basic Roman Numerals: Roman numerals use letters like I, V, X, L, C, D, and M.
- Subtraction Rule: Smaller numerals can be subtracted from larger ones, but only I, X, and C are used for subtraction in Roman numeral rules.
- Why V Cannot Be Subtracted: V is not used in subtraction because Roman numeral rules only allow I before V and X, and only one smaller numeral can precede a larger one to indicate subtraction.
- Conclusion: Thus, V can never be subtracted from any other numeral.

- Roman Numerals Basics: Roman numerals use letters I, V, X, L, C, D, and M. Each letter has a specific value (e.g., I = 1, V = 5, X = 10).
- Construction Rules:
- Smaller numbers before larger numbers are subtracted (e.g., IX = 9).
- Larger numbers before smaller numbers are added (e.g., XV = 15).
- Meaningless Numeral:
- IXIV is incorrect because it violates construction rules. Subtraction (IX) should not be followed by another subtraction (IV); instead, both should be combined correctly as XIII (13).

25 + 14 = 39 = XXV + XIV = XXXIX  
∴ 4 symbols are needed.

0 has no Roman numeral.

- Statement A: C - X = XC
- C (100) - X (10) = XC (90). This is correct.
- Statement B: XI - IX = XX
- XI (11) - IX (9) = II (2), not XX (20). This is incorrect.
- Statement C: DC - C = D
- DC (600) - C (100) = D (500). This is correct.
- Statement D: LXI - LIX = II
- LXI (61) - LIX (59) = II (2). This is correct.

- Conclusion: Statement B is the incorrect one.

Let's evaluate each statement by converting Roman numerals to Arabic numbers:

• A: DCVI = 606. Thus, 516 < 606 is correct.
• B: CCLVII = 257. Thus, 256 ≠ 257.
• C: CDVIII = 408. Thus, 408 = 408.
• D: MD = 1500. Thus, 1005 < 1500.

Only statement A is correct, as all others contain inaccuracies in number comparisons.

The greatest number formed is DCLX = 660 and the least is CDXL = 440. Their difference is 220 = CCXX.

To determine which number has a Roman numeral equivalent made with 10 matchsticks, we convert each number into Roman numerals:

• 39: XXXIX (11 sticks: X=2, X=2, X=2, I=1, X=2, V=2)
• 27: XXVII (8 sticks: X=2, X=2, V=2, I=1, I=1)
• 37: XXXVII (10 sticks: X=2, X=2, X=2, V=2, I=1, I=1)
• 35: XXXV (9 sticks: X=2, X=2, X=2, V=2)

Thus, 37 (XXXVII) requires 10 matchsticks, making C the correct answer.

The greatest 3-digit number is 999 = 900 + 90 + 9 = (1000 − 100) + (100 − 10) + (10 − 1)
999 = (M−C)+(C−X)+(X−I)
Rewrite the terms after subtraction,
⇒999 = CM+XC+IX
Join the terms,
⇒ 999 = CMXCIX.