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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

 ${\rm{n}}$
 ${\rm{n}} + 1$
 ${\rm{k}} \times {\rm{n,}}$ where k is a function of n
 ${\rm{n}} + \left( {\frac{2}{7}} \right)$

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

 16
 12
 11
 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

 xyz2is odd
 (x – y)2z is even
 (x + y – z)2(x + y) is even
 (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
 4
 5
 10

Question 5:
Let N = 1421 × 1423 × 1425. What is the remainder when N is divided by 12?
Topic: Divisibility

 0
 9
 3
 6

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