CAT 2003 Slot 2 — QA Question 50
Answer the following question based on the information given below.
The seven basic symbols in a certain numeral system and their respective values are as follows:
I = 1, V = 5, X = 10, L = 50, C = 100, D = 500, and M = 1000
In general, the symbols in the numeral system are read from left to right, starting with the symbol representing the largest value; the same symbol cannot occur continuously more than three times; the value of the numeral is the sum of the values of the symbols.
For example, XXVII = 10 + 10 + 5 + 1 + 1 = 27.
An exception to the left-to-right reading occurs when a symbol is followed immediately by a symbol of greater value; then, the smaller value is subtracted from the larger.
For example, XLVI = (50 – 10) + 5 + 1 = 46.
Which of the following can represent the numeral for 1995?
a. MCMLXXV
b. MCMXCV
c. MVD
d. MVM
Answer & solution
- A
Only (a) and (b)
- B
Only (c) and (d)
Only (b) and (d)
- D
Only (d)
Option (a): MCMLXXV
= 1000 + (1000 – 100) + 50 + 10 + 10 + 5
= 1000 + 900 + 50 + 25 = 1975
Option (b): MCMXCV
= 1000 + (1000 – 100) + (100 – 10) + 5
= 1000 + 900 + 90 + 5 = 1995
Option (c): MVD
= 1000 + (500 – 5) = 1000 + 495 = 1495
Option (d): MVM
= 1000 + (1000 – 5) = 1000 + 995 = 1995
Options (b) and (d) give 1995.
Hence, option (c).