# 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.

1. #### 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

2. #### CAT Number Theory - Binomial Theorem

What is the remainder when (13100 + 17100) is divided by 25?

1. 0
2. 2
3. 4
4. 11

3. #### 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

4. #### 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

5. #### CAT Remainders - Factorization Properties

What is the remainder when we divide 390 + 590 by 34?

1. 0
2. 17
3. 33
4. 1

6. #### 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

7. #### 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

8. #### 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

9. #### 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

10. #### 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

11. #### 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

12. #### 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

13. #### 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

14. #### 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

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.

1. #### 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 __________.

2. #### 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 ###### Prepare for CAT 2022 with 2IIM's Daily Preparation Schedule ###### Know all about CAT Exam Syllabus and what to expect in CAT ###### Best CAT Online Coaching Try upto 40 hours for free Learn from the best! ###### Already have an Account? ###### CAT Coaching in ChennaiCAT 2022 Classroom Batches Starting Now! @Gopalapuram ###### Best CAT Coaching in Chennai Introductory offer of 5000/- Attend a Demo Class ###### Best Indore IPM & Rohtak IPM CoachingSignup and sample 9 full classes for free. Register now! ## CAT Online Coaching | CAT Number Systems questions Videos On YouTube #### Other useful sources for Number System Questions | Number Theory Remainders Sample Questions ##### Where is 2IIM located? 2IIM Online CAT Coaching A Fermat Education Initiative, 58/16, Indira Gandhi Street, Kaveri Rangan Nagar, Saligramam, Chennai 600 093 ##### How to reach 2IIM? Phone:$91) 44 4505 8484
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