Basic Symbol Numeral System

CAT 2003 Slot 1 · QA · Easy · Number Systems

Passage / data set

Directions for questions 51 to 53: Answer the questions on the basis of 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\text{I} = 1, \text{V} = 5, \text{X} = 10, \text{L} = 50, \text{C} = 100, \text{D} = 500 \text{ and } \text{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\text{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=(5010)+5+1=46\text{XLVI} = (50 - 10) + 5 + 1 = 46.

Question 1 of 3

The value of the numeral MDCCLXXXVII is

  1. A.

    1687

  2. B.

    1787

  3. C.

    1887

  4. D.

    1987

Answer

B

Explanation

MDCCLXXXVII=1000+500+100+100+50+10+10+10+5+1+1=1787\text{MDCCLXXXVII} = 1000 + 500 + 100 + 100 + 50 + 10 + 10 + 10 + 5 + 1 + 1 = 1787.

Question 2 of 3

The value of the numeral MCMXCIX is

  1. A.

    1999

  2. B.

    1899

  3. C.

    1989

  4. D.

    1889

Answer

A

Explanation

MCMXCIX=1000+(1000100)+(10010)+(101)=1000+900+90+9=1999\text{MCMXCIX} = 1000 + (1000 - 100) + (100 - 10) + (10 - 1) = 1000 + 900 + 90 + 9 = 1999.

Question 3 of 3

Which of the following represent the numeral for 1995? I. MCMLXXV II. MCMXCV III. MVD IV. MVM

  1. A.

    Only I and II

  2. B.

    Only III and IV

  3. C.

    Only II and IV

  4. D.

    Only IV

Answer

C

Explanation

II: MCMXCV=1000+900+90+5=1995\text{MCMXCV} = 1000 + 900 + 90 + 5 = 1995. IV: MVM=1000+(10005)=1995\text{MVM} = 1000 + (1000 - 5) = 1995. Hence, II and IV are correct.

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