**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

[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

[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

[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

[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

[1] Only I and II

[2] Only III and IV

[3] Only II and IV

[4] Only IV

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