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# CAT Number system Practice Problems Set 02

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

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

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] xyz2is odd
[2] (x – y)2z is even
[3] (x + y – z)2(x + y) is even
[4] (x – y)(y + z)(x + y – z) is odd

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

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

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