1EasyMCQ
Which of the following cannot be the difference between a two-digit number and the number formed by reversing its digits?
- A
- B
- C
- D
Number System Questions for CAT
Preview 20 questions below, then sign up free to solve them in practice mode with worked solutions, and to reach all 1,350.
Verified questions1,350
Worked solutions in practice mode73 from CAT papers
329 easy638 medium383 hard
Number System is where most CAT preparation starts, and it rewards practice more directly than almost any other topic, the underlying ideas are few (divisibility, remainders, factors, base systems, last digits) but the ways they are combined into a question are effectively unlimited. That is why a large bank matters here more than a long theory chapter. Working through several hundred questions is what turns remainder theorems from something you can recite into something you can recognise under time pressure.
20 free Number System questions
2EasyMCQ
The least number which can be added to 763 so that it is completely divisible by 57 is
- A
35
- B
22
- C
15
- D
25
3EasyTITA
LCM of two numbers is 421. What is HCF?
4EasyMCQ
For a natural number N, if N^3 is divisible by 2, which of the following statements is incorrect?
- A
N^2 is divisible by 4
- B
N is divisible by 2
- C
N^4 is divisible by 16
- D
None of these
5EasyMCQ
The highest power of 13 dividing 1000! is?
- A
76
- B
81
- C
78
- D
79
6EasyMCQ
What is the sum of all factors of the number ?
- A
- B
- C
- D
7MediumMCQ
If is divisible by , determine the value of .
A.
B.
C.
D.
- A
A:
- B
B:
- C
C:
- D
D:
8MediumMCQ
The page numbers of a book are counted starting from 1. Due to an error, the digits of a two-digit page number were swapped, resulting in a total of 5022. What is the page number that had its digits swapped?
- A
72
- B
19
- C
29
- D
Can't be determined
9MediumMCQ
What is the sum of the last three digits of the number ?
A.
B.
C.
D.
- A
A:
- B
B:
- C
C:
- D
D:
10MediumTITA
How many integers exist such that not only are they multiples of 904 but also are factors of 904 ?
11MediumTITA
The sum of the first two natural numbers, each having exactly 12 factors (including 1 and the number itself), is
12MediumMCQ
What is the remainder when is divided by ?
- A
0
- B
1
- C
6
- D
4
13MediumMCQ
What is the count of natural numbers less than 1001 that are divisible by 4 but not by 12?
- A
165
- B
167
- C
168
- D
192
14MediumMCQ
What is the highest power of that divides ?
- A
48
- B
49
- C
50
- D
51
15HardMCQ
In an assembly, students arrange themselves in a square formation, leaving 5 students remaining. In a rectangle with 9 more rows than columns, all students fit perfectly. How many students are there?
- A
Greater than 200 and less than 300
- B
Greater than 600 and less than 700
- C
Greater than 500 and less than 600
- D
None of these
16HardMCQ
There are 8 natural numbers with a sum of 289, out of which only one is odd. If the average of the 4 highest numbers exceeds the average of the 4 lowest numbers by 46.25, find the highest possible average of the lowest and highest numbers. Also, no three of the numbers can be equal.
- A
92
- B
102
- C
101
- D
51
17HardMCQ
Evaluate the expression , where represents the base and is a digit in base . Determine the value of .
- A
- B
- C
- D
- E
None of the above
18HardMCQ
What are the last two non-zero digits of ?
- A
- B
- C
- D
19HardMCQ
What is the remainder when is calculated?
- A
1
- B
74
- C
56
- D
100
20HardMCQ
N is an integer such that the product of all its factors equals N^2 and the sum of all proper factors equals 31. How many possible values of N exist?
- A
2
- B
3
- C
4
- D
5
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Number System for CAT, answered
What CAT asks in Number System, the mistakes that cost the most marks, and how to practise it.
In practice: divisibility rules, factors and multiples, HCF and LCM, remainders (including cyclicity and the standard remainder theorems), last digits, number of trailing zeroes, base systems, and factorials. CAT publishes no official syllabus, so this list describes what the papers have consistently tested rather than a prescribed set.
It appears in every paper and, more importantly, it underpins other topics, permutation and combination questions frequently turn on a divisibility or factor argument. Even when the question is labelled something else, Number System is often what actually solves it.
Do them in a single block rather than scattered, because the standard patterns only become visible once you have seen several in a row. When you get one wrong, redo it from scratch rather than reading the solution first, remainder problems are unusually easy to follow along with and still not be able to reproduce.
Every question here has been checked against a worked solution before being published, and anything without a complete solution is not shown at all. The bank mixes questions written for CAT-level practice with questions from actual CAT papers; the previous-year questions are collected separately under CAT PYQs. The solutions themselves open in practice mode once you sign up, which is free.