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

[1] \({\rm{n}}\)
[2] \({\rm{n}} + 1\)
[3] \({\rm{k}} \times {\rm{n,}}\) where k is a function of n
[4] \({\rm{n}} + \left( {\frac{2}{7}} \right)\)
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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?

[1] 16
[2] 12
[3] 11
[4] 13
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Question 3:
Let x, y and z be distinct integers, that are odd and positive. Which one of the following statements cannot be true?

[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
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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?

[1] 1
[2] 4
[3] 5
[4] 10
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Question 5:
Let N = 1421 × 1423 × 1425. What is the remainder when N is divided by 12?

[1] 0
[2] 9
[3] 3
[4] 6
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