CAT Questions | CAT Number Systems Questions | 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?

A. 7

B. 29

C. 16

D. 13

Correct Answer
Choice B
29
CAT Number Theory - Binomial Theorem

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

A. 0

B. 2

C. 4

D. 11

Correct Answer
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?

A. 2

B. 0

C. 1

D. 3

Correct Answer
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?

A. 3

B. 5

C. 4

D. 2

Correct Answer
Choice B
5
CAT Remainders - Factorization Properties

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

A. 0

B. 17

C. 33

D. 1

Correct Answer
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?

A. 1, 5, 7 and 11

B. 1 and 5

C. 5, 9, and 11

D. 1 and 11

Correct Answer
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?

A. 8

B. 12

C. 9

D. 15

Correct Answer
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?

A. 32

B. 36

C. 24

D. 19

Correct Answer
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?

A. 65

B. 96

C. 125

D. More than one value is possible

Correct Answer
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?

A. 3

B. 2

C. 5

D. 4

Correct Answer
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?

A. 0

B. 8

C. 1

D. 5

Correct Answer
Choice D
5
CAT Number Systems - Divisibility - Large Number

Given a number, N = 55⁵ + 17⁵ – 72⁵, then which of the following is true?

A. N is divisible by both 7 and 13

B. N is divisible by both 3 and 17

C. N is divisible by 17 but not 3

D. N is divisible by 11 but not 17

Correct Answer
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?

A. 206

B. 256

C. 274

D. 189

Correct Answer
Choice B
256
CAT Remainder - Large number

If N = (24³ + 25³ + 26³ + 27³), then N divided by 102 leaves a remainder of?

A. 18

B. 12

C. 1

D. 0

Correct Answer
Choice D
0

CAT Questions | CAT Number Systems Questions | Remainders

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