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# CAT Number system Practice Problems Set 15

Question 1:
For a positive integer n, let pn denote the product of the digits of n and sn denote the sum of the digits of n. The number of integers between 10 and 1000 for which pn + sn = n is
Topic: Basics

[1] 81
[2] 16
[3] 18
[4] 9

Question 2:
Let S be a set of positive integers such that every element n of S satisfies the conditions

I. 1000 ≤n ≤1200

II. Every digit in n is odd

Then how many elements of S are divisible by 3?

Topic: Divisibility

[1] 9
[2] 10
[3] 11
[4] 12

Question 3:
A rectangular floor is fully covered with square tiles of identical size. The tiles on the edges are white and the tiles in the interior are red. The number of white tiles is the same as the number of red tiles.

A possible value of the number of tiles along one edge of the floor is

Topic: Factors

[1] 10
[2] 12
[3] 14
[4] 16

Question 4:
The sum of four consecutive two-digit odd numbers, when divided by 10, becomes a perfect square. Which of the following can possibly be one of these four numbers?
Topic: Divisibility

[1] 21
[2] 25
[3] 41
[4] 67

Question 5:
The number of employees in Obelix Menhir Co. is a prime number and is less than 300. The ratio of the number of employees who are graduates and above, to that of employees who are not, can possibly be:
Topic: Basics

[1] 101 : 88
[2] 87 : 100
[3] 110 : 111
[4] 85 : 98

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