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# CAT Number system Practice Problems Set 11

Question 1:
The number of positive integers n in the range 12 ≤ n ≤ 40 such that the product (n −1)(n − 2) 3.2.1 is not divisible by n is
Topic: Remainders

[1] 5
[2] 7
[3] 13
[4] 14

Question 2:
Let T be the set of integers {3, 11, 19, 27, … 451, 459, 467} and S be a subset of T such that the sum of no two elements of S is 470. The maximum possible number of elements in S is
Topic: Basics

[1] 32
[2] 28
[3] 29
[4] 30

Question 3:
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.

The value of the numeral MDCCLXXXVII is 1687

Topic: Basics

[1] 1687
[2] 1787
[3] 1887
[4] 1987

Question 4:
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.

The value of the numeral MCMXCIX is

Topic: Basics

[1] 1999
[2] 1899
[3] 1989
[4] 1889

Question 5:
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 represent the numeral for 1995?

I. MCMLXXV

II. MCMXCV

III. MVD

IV. MVM

Topic: Basics

[1] Only I and II
[2] Only III and IV
[3] Only II and IV
[4] Only IV

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