**Question 1:**

The integers 34041 and 32506, when divided by a three-digit integer n, leave the same remainder.

What is the value of n?

Topic: HCF LCM

[1] 289

[2] 367

[3] 453

[4] 307

**Question 2:**

Each of the numbers x

_{1}, x

_{2},, x

_{n},n ≥ 4, is equal to 1 or –1. Suppose

\({x_1}{x_2}{x_3}{x_4} + {x_2}{x_3}{x_4}{x_5} + {x_{n - 3}}{x_{n - 2}}{x_{n - 1}}{x_n} + ... + {x_{n - 2}}{x_{n - 1}}{x_n}{x_1} + {x_{n - 1}}{x_n}{x_1}{x_2} + {x_n}{x_1}{x_2}{x_3} = 0,\) then

Topic: Basics

[1] n is even

[2] n is odd

[3] n is an odd multiple of 3

[4] n is prime

**Question 3:**

A, B and C are three numbers. Let

@ (A, B) = Average of A and B,

/ (A, B) = Product of A and B, and

× (A, B) = The result of dividing A by B.

The sum of A and B is given by

Topic: Basics

[1] / (@ (A, B), 2)

[2] × (@ (A, B), 2)

[3] @ (/ A, B), 2)

[4] @ (× (A, B), 2)

**Question 4:**

A, B and C are three numbers. Let

@ (A, B) = Average of A and B,

/ (A, B) = Product of A and B, and

× (A, B) = The result of dividing A by B.

Average of A, B and C is given by

Topic: Basics

[1] @ (/ (@ (/ (B, A), 2), C), 3)

[2] × (@ (/ (@ (B, A), 3), C), 2)

[3] / (×(× (@ (B, A), 2), C), 3)

[4] / (× (@ (/ (@ (B, A) 2), C), 3), 2)

**Question 5:**

Let N = 55

^{3}+ 17

^{3}– 72

^{3}. N is divisible by

Topic: Divisibility

[1] both 7 and 13

[2] both 3 and 13

[3] both 17 and 7

[4] both 3 and 17

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