**Question 1:**

Consider a sequence of seven consecutive integers. The average of the first five integers is n. The average of all the seven integers is

Topic: Basics

[1] \({\rm{n}}\)

[2] \({\rm{n}} + 1\)

[3] \({\rm{k}} \times {\rm{n,}}\) where k is a function of n

[4] \({\rm{n}} + \left( {\frac{2}{7}} \right)\)

**Answer: **Option: 2

**Question 2:**

Let S be the set of integers x such that

I. 100 ≤ x ≤ 200 ,

II. x is odd and

III. x is divisible by 3 but not by 7.

How many elements does S contain?

Topic: Divisibility

[1] 16

[2] 12

[3] 11

[4] 13

**Answer: **Option: 4

**Question 3:**

Let x, y and z be distinct integers, that are odd and positive. Which one of the following statements cannot be true?

Topic: Basics

[1] xyz

^{2}is odd

[2] (x – y)

^{2}z is even

[3] (x + y – z)

^{2}(x + y) is even

[4] (x – y)(y + z)(x + y – z) is odd

**Answer: **Option: 4

**Question 4:**

Let S be the set of prime numbers greater than or equal to 2 and less than 100. Multiply all elements of S. With how many consecutive zeros will the product end?

Topic: Basics

[1] 1

[2] 4

[3] 5

[4] 10

**Answer: **Option: 1

**Question 5:**

Let N = 1421 × 1423 × 1425. What is the remainder when N is divided by 12?

Topic: Divisibility

[1] 0

[2] 9

[3] 3

[4] 6

**Answer: **Option: 3

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