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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 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