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.

In the Roman numeral system, there is no symbol for zero (0). The other numbers—13 (XIII), 27 (XXVII), and 39 (XXXIX)—all have valid Roman numeral representations.

Therefore, the correct answer is A, as 0 does not have a 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.