# Number System Questions for CAT

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Number systems is the most important topic for CAT exam. The number of questions asked from number systems in CAT is very high and also this topic is the most basic topic in CAT Syllabus. The questions will vary from easy to difficult and learning number systems tricks for CAT will be very helpful.

# Number System Questions for CAT:

Question 1:

Five-digit numbers are formed using only 0, 1, 2, 3, 4 exactly once. What is the difference between the maximum and minimum number that can be formed?

a) 19800
b) 41976
c) 32976
d) None of these

Question 2:

A is the set of positive integers such that when divided by 2, 3, 4, 5, 6 leaves the remainders 1, 2, 3, 4, 5 respectively. How many integers between 0 and 100 belong to set A?

a) 0
b) 1
c) 2
d) None of these

Question 3:

Twenty-seven persons attend a party. Which one of the following statements can never be true?

a) There is a person in the party who is acquainted with all the twenty-six others.
b) Each person in the party has a different number of acquaintances.
c) There is a person in the party who has an odd number of acquaintances.
d) In the party, there is no set of three mutual acquaintances.

Question 4:

P, Q and R are three consecutive odd numbers in ascending order. If the value of three times P is 3 less than two times R, find the value of R.

a) 5
b) 7
c) 9
d) 11

Question 5:

A positive whole number M less than 100 is represented in base 2 notation, base 3 notation, and base 5 notation. It is found that in all three cases the last digit is 1, while in exactly two out of the three cases the leading digit is 1. Then M equals

a) 31
b) 63
c) 75
d) 91

Answers and Solutions for Number System Questions for CAT:

Solutions:

Maximum five digit number which can be formed by using numbers is 43210
And minimum five digit number = 10234
Difference = 43210 – 10234 = 32976

Let the number ‘n’ belong to the set A.
Hence, the remainder when n is divided by 2 is 1
The remainder when n is divided by 3 is 2
The remainder when n is divided by 4 is 3
The remainder when n is divided by 5 is 4 and
The remainder when n is divided by 6 is 5
So, when (n+1) is divisible by 2,3,4,5 and 6.
Hence, (n+1) is of the form 60k for some natural number k.
And n is of the form 60k-1
Between numbers 0 and 100, only 59 is of the form above and hence the correct answer is 1

From the options a, c and d all can possibly occur. Hence option b. Besides, if all people have different number of acquaintances, then first person will have 26 acquaintance, second person will have 25 acquaintance, third person will have 24 and so on till 27 th person will have 0 acquaintance. 0 acquaintance is practically not possible.