CAT Questions | CAT Number Theory: Remainders Questions

CAT Quantitative Aptitude | CAT Number Theory Remainders

A CAT Number Systems: Remainders question that appears in the Quantitative Aptitude section of the CAT Exam broadly tests an aspirant on the concepts - Remainder Theory, Successive Remainders, Test of Divisibility and so on. In CAT Exam, one can generally expect to get approx. 1 question from CAT Number Systems: Remainders. Make use of 2IIMs Free CAT Questions, provided with detailed solutions and Video explanations to obtain a wonderful CAT score. If you would like to take these questions as a Quiz, head on here to take these questions in a test format, absolutely free.

CAT Number Theory: Remainders - Sum of Digits

The sum of the digits of a number N is 23. The remainder when N is divided by 11 is 7. What is the remainder when N is divided by 33?
1. 7
2. 29
3. 16
4. 13
Choice B
29
CAT Number Theory - Binomial Theorem

What is the remainder when (13¹⁰⁰ + 17¹⁰⁰) is divided by 25?
1. 0
2. 2
3. 4
4. 11
Choice B
2
CAT Number Theory Remainders

A number when divided by 18 leaves a remainder 7. The same number when divided by 12 leaves a remainder n. How many values can n take?
1. 2
2. 0
3. 1
4. 3
Choice A
2
CAT Remainders

N leaves a remainder of 4 when divided by 33, what are the possible remainders when N is divided by 55?
1. 3
2. 5
3. 4
4. 2
Choice B
5
CAT Remainders - Factorization Properties

What is the remainder when we divide 3⁹⁰ + 5⁹⁰ by 34?
1. 0
2. 17
3. 33
4. 1
Choice A
0
CAT Remainders - Squares

N² leaves a remainder of 1 when divided by 24. What are the possible remainders we can get if we divide N by 12?
1. 1, 5, 7 and 11
2. 1 and 5
3. 5, 9, and 11
4. 1 and 11
Choice A
1, 5, 7 and 11
CAT Remainders, coprime numbers

A prime number p greater than 100 leaves a remainder q on division by 28. How many values can q take?
1. 8
2. 12
3. 9
4. 15
Choice B
12
CAT Remainders and LCM

How many positive integers are there from 0 to 1000 that leave a remainder of 3 on division by 7 and a remainder of 2 on division by 4?
1. 32
2. 36
3. 24
4. 19
Choice B
36
CAT Remainders - Basics

Three numbers leave remainders of 43, 47 and 49 on division by N. The sum of the three numbers leaves a remainder 9 on division by N. What are the values N can take?
1. 65
2. 96
3. 125
4. More than one value is possible
Choice D
More than one value is possible
CAT Remainders

A number leaves a remainder 3 on division by 14, and leaves a remainder k on division by 35. How many possible values can k take?
1. 3
2. 2
3. 5
4. 4
Choice C
5
CAT Number Systems: Remainders - Large number

Consider a large number N = 1234567891011121314………979899100. What is the remainder when first 100 digits of N is divided by 9?
1. 0
2. 8
3. 1
4. 5
Choice D
5
CAT Number Systems - Divisibility - Large Number

Given a number, N = 55⁵ + 17⁵ – 72⁵, then which of the following is true?
1. N is divisible by both 7 and 13
2. N is divisible by both 3 and 17
3. N is divisible by 17 but not 3
4. N is divisible by 11 but not 17
Choice B
N is divisible by both 3 and 17
CAT Number Systems - Same remainder

The integers 573921 and 575713 when divided by a 3 digit number leave the same remainder. What is that 3 digit number?
1. 206
2. 256
3. 274
4. 189
Choice B
256
CAT Remainder - Large number

If N = (24³ + 25³ + 26³ + 27³), then N divided by 102 leaves a remainder of?
1. 18
2. 12
3. 1
4. 0
Choice D
0

The Questions that follow, are from actual CAT papers. If you wish to take them separately or plan to solve actual CAT papers at a later point in time, It would be a good idea to stop here.

CAT 2022 Slot 3 - QA
A school has less than 5000 students and if the students are divided equally into teams of either 9 or 10 or 12 or 25 each, exactly 4 are always left out. However, if they are divided into teams of 11 each, no one is left out. The maximum number of teams of 12 each that can be formed out of the students in the school is
150

The Questions that follow, are from actual IPMAT papers. If you wish to take them separately or plan to solve actual IPMAT papers at a later point in time, It would be a good idea to stop here.

IPMAT 2020 Question Paper - IPM Indore Quants
In a division problem, product of quotient and the remainder is 24 while their sum is 10. If the divisor is 5 then dividend is __________.
34
IPMAT 2019 Question Paper - IPM Indore Quants
The remainder when \29^{29^{29}}\\) is divided by 9 is
1. 1
2. 2
3. 3
4. 4
Choice B
2