1 
A twodigit number is such that it is the product of two distinct perfect squares. The tens digit, u...
CAT
Quantitative Ability
Algebra
Sequences and Series
AP, GP
AP
Theory of Numbers
Numbers, Properties & Operations

2 
In a number system the product of 44 and 11 is 3414. Find the base in which these numbers are writte...
CAT
Quantitative Ability
Theory of Numbers
Base System

3 
The number ( 2324X1013 )7 is converted to base 10 then divided by 6. It leaves no rem...
CAT
Quantitative Ability
Theory of Numbers
Base System

4 
Which of the points indicated by the labels P, Q, R, S, and T on the number line below has the secon...
CAT
Quantitative Ability
Theory of Numbers
Numbers, Properties & Operations

5 
For every natural number n , the highest number that n×( n 2 −1)×(5n+2)&n...
CAT
Quantitative Ability
Theory of Numbers
Numbers, Properties & Operations

6 
For a positive integer n, let Pn denote the product of the digits of n and Sn denote the s...
CAT
Quantitative Ability
Theory of Numbers
Numbers, Properties & Operations

7 
The units digit of ( 12345k ) 72 is 6. Among the given options, what can be the value of k? ...
CAT
Quantitative Ability
Theory of Numbers
Remainders
Properties of Remainders

8 
What is the least number which when divided by 12, 18, 36 and 45 leaves remainders 8, 14, 32 and 41,...
CAT
Quantitative Ability
Theory of Numbers
Remainders
Properties of Remainders

9 
Which of the following is/are true: Statement A: If a number is divisible by both 2 and 3, then the...
CAT
Quantitative Ability
Theory of Numbers
Numbers, Properties & Operations
Representation of Numbers
Families of Integers

10 
If k and m are natural numbers, then the remainder when (3k + ( 1)m)6 is divided by 9 : ...
CAT
Quantitative Ability
Theory of Numbers
Remainders

11 
How many 3digit numbers are there which are divisible by only 3 distinct numbers? Type in you...
CAT
Quantitative Ability
Theory of Numbers
Factors, Multiples

12 
What is the least possible number which when divided by 13 leaves a remainder 3 and when it is divid...
CAT
Quantitative Ability
Theory of Numbers
Factors, Multiples

13 
The number 2006! is written in base 22. How many trailing zeroes are there in the number? Type in y...
CAT
Quantitative Ability
Theory of Numbers
Base System

14 
Find the remainder when 752 is divided by 2402. Type in your answer as an integer. For example...
CAT
Quantitative Ability
Theory of Numbers
Remainders

15 
What is the remainder when 123 × 124 × 125 is divided by 9?
CAT
Quantitative Ability
Theory of Numbers
Remainders

16 
How many numbers between 11 and 1111 which when divided by 9 leave a remainder of 6 and when di...
CAT
Quantitative Ability
Theory of Numbers
Factors, Multiples
HCF, LCM
Application of Remainders
Remainders

17 
The last digit of the number obtained by multiplying the numbers 81⋅82⋅83⋅84⋅85...
CAT
Quantitative Ability
Theory of Numbers
Remainders
Properties of Remainders

18 
Out of first 300 even natural numbers, how many numbers have even number of factors? Type in your a...
CAT
Quantitative Ability
Theory of Numbers
Factors, Multiples

19 
Find the remainder when 270 is divided by 96.
CAT
Quantitative Ability
Theory of Numbers
Remainders

20 
Let n>1, be a positive integer. Then the largest number m, such that ( nm + 1) divides ( 1 ...
CAT
Quantitative Ability
Theory of Numbers
Numbers, Properties & Operations

21 
The least number which is always divisible by 36 and 32 is: Type in your answer as an integer. For ...
CAT
Quantitative Ability
Theory of Numbers
Numbers, Properties & Operations
Representation of Numbers
Families of Integers

22 
Choose from the options the correct Number families in Column 2 to the group of numbers in Column 1 ...
CAT
Quantitative Ability
Theory of Numbers
Numbers, Properties & Operations

23 
Comment on the following statements: Statement A: Let x be a rational number whose decimal expansio...
CAT
Quantitative Ability
Theory of Numbers
Numbers, Properties & Operations
Representation of Numbers
Classification of numbers

24 
What is the remainder when 683 + 883 is divided by 49? Type in your answer as an integer. For examp...
CAT
Quantitative Ability
Theory of Numbers
Remainders

25 
What is the remainder when 3040 is divided by 7? Type in your answer as an integer. For example, if...
CAT
Quantitative Ability
Theory of Numbers
Remainders

26 
Consider the following statements: Statement A: Prime numbers are numbers with exactly two factors:...
CAT
Quantitative Ability
Theory of Numbers
Numbers, Properties & Operations

27 
The digit in the units place of the number represented by ( 7 95 − 3 58 ) is Type in...
CAT
Quantitative Ability
Theory of Numbers
Remainders
Properties of Remainders

28 
If we divide any positive integer by 3, the possible remainders are 0, 1 and 2. Thus the t...
CAT
Quantitative Ability
Theory of Numbers
Numbers, Properties & Operations
Representation of Numbers
Families of Integers

29 
Express 0.5 85 ¯ in p/q form ...
CAT
Quantitative Ability
Theory of Numbers
Numbers, Properties & Operations

30 
What is the remainder when 1! + 2! + 3! + …. + 100! is divided by 5? Type in your answer as ...
CAT
Quantitative Ability
Theory of Numbers
Remainders

31 
What is the remainder when (81)21 + (27)21 + (9)21 + (3)21 + 1 is divided by 320 + 1? Type in your ...
CAT
Quantitative Ability
Theory of Numbers
Remainders

32 
The remainder when 22005 is divided by 13 is: Type in your answer as an integer. For example, if yo...
CAT
Quantitative Ability
Theory of Numbers
Advanced Theorems
Wilson's Theorem

33 
The set of the squares of all integers can be represented as
CAT
Quantitative Ability
Theory of Numbers
Numbers, Properties & Operations
Representation of Numbers
Families of Integers

34 
It is given that N is a recurring decimal given by N=0.abc ¯ where at most two of a, b, c ar...
CAT
Quantitative Ability
Theory of Numbers
Numbers, Properties & Operations
Representation of Numbers
Classification of numbers

35 
A forester wants to plant 44 apple trees, 66 banana trees and 110 mango trees in equal rows (in term...
CAT
Quantitative Ability
Theory of Numbers
Factors, Multiples
HCF, LCM

36 
Total number of factors of a number is 24 and the sum of its 3 prime factors out of 4, is 25. The pr...
CAT
Quantitative Ability
Theory of Numbers
Factors, Multiples

37 
Which one of the following statements is not correct?
CAT
Quantitative Ability
Theory of Numbers
Numbers, Properties & Operations
Representation of Numbers
Classification of numbers

38 
How many odd numbers in the range between 10 and 100, inclusive, are not divisible by 3? Type in yo...
CAT
Quantitative Ability
Theory of Numbers
Numbers, Properties & Operations

39 
Find the remainder when 21990 is divided by 1990. Type in your answer as an integer. For examp...
CAT
Quantitative Ability
Theory of Numbers
Remainders

40 
What is the last remainder when 223 is successively divided by 4, 5 and 6?
CAT
Quantitative Ability
Theory of Numbers
Numbers, Properties & Operations
Representation of Numbers
Families of Integers

41 
How many natural numbers are factors of exactly one of the following two numbers? 675 and 1080 Typ...
CAT
Quantitative Ability
Theory of Numbers
Factors, Multiples

42 
If a 3 digit number 'abc' has 2 factors (where a, b, and c are integers), how many factors d...
CAT
Quantitative Ability
Theory of Numbers
Factors, Multiples

43 
The least number which is a perfect square and has ...
CAT
Quantitative Ability
Theory of Numbers
Factors, Multiples

44 
Find the least number (greater than 20) which is a factor of 7 101 + 18 101 Type in your...
CAT
Quantitative Ability
Theory of Numbers
Remainders
Properties of Remainders

45 
( n 2 +5n+6) is a multiple of 6, where n is a natural number less than 100. How many valu...
CAT
Quantitative Ability
Theory of Numbers
Numbers, Properties & Operations

46 
In how many ways can 1146600 be written as a product of...
CAT
Quantitative Ability
Theory of Numbers
Factors, Multiples
Properties of Factors

47 
If a five digit number N is such that the sum of its digits is 29, can N be the square of an integer...
CAT
Quantitative Ability
Theory of Numbers
Numbers, Properties & Operations

48 
How many times the HCF of the fractions 4 9  ,  8 27  , 10 63 is...
CAT
Quantitative Ability
Theory of Numbers
Factors, Multiples
HCF, LCM

49 
A test has 80 questions. There is one mark for a correct answer, while there is a negative penalty o...
CAT
Quantitative Ability
Theory of Numbers
Numbers, Properties & Operations

50 
Find the remainder when 3340 is divided by 341. Type in your answer as an integer. For example...
CAT
Quantitative Ability
Theory of Numbers
Remainders

51 
What is the remainder when 2256 divided by 17?
CAT
Quantitative Ability
Theory of Numbers
Remainders

52 
Which of the following can never be true?
CAT
Quantitative Ability
Theory of Numbers
Factors, Multiples
HCF, LCM

53 
A six digit number which consists of only one digit either 1, 2, 3, 4, 5, 6, 7, 8 or 9, for exa...
CAT
Quantitative Ability
Theory of Numbers
Numbers, Properties & Operations

54 
Find the remainder when 43444 is divided by 9. Type in your answer as an integer. For example,...
CAT
Quantitative Ability
Theory of Numbers
Remainders

55 
What is the HCF of 4 6 , 3 9 , 6 5 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gz...
CAT
Quantitative Ability
Theory of Numbers
Factors, Multiples
HCF, LCM

56 
Find the largest number which will always divide the sum of cubes of three consecutive positive...
CAT
Quantitative Ability
Theory of Numbers
Factors, Multiples

57 
How many values can a natural number 'n' take if n! is a multiple of 230 but ...
CAT
Quantitative Ability
Theory of Numbers
Factors, Multiples
Numbers, Properties & Operations

58 
If a number N is divided by 17, then which of the following is/are true A: The number of possible&n...
CAT
Quantitative Ability
Theory of Numbers
Numbers, Properties & Operations
Representation of Numbers
Families of Integers

59 
The HCF of x and y is H. Find the HCF of (x – y) and (x3 + y3)/(x2 – xy + y2). ...
CAT
Quantitative Ability
Theory of Numbers
Factors, Multiples
HCF, LCM

60 
Is there any positive integer 'n' possible such which can divide ( 2n + 3n&nb...
CAT
Quantitative Ability
Theory of Numbers
Remainders

61 
What is the number of zeroes at the end of the product 101×102×103×104×105...
CAT
Quantitative Ability
Theory of Numbers
Factors, Multiples
Numbers, Properties & Operations
Probability

62 
How many three digit numbers are there which when divided by 9 and 8 give a remainder of 8 and 7? T...
CAT
Quantitative Ability
Theory of Numbers
Factors, Multiples
HCF, LCM

63 
The units digit of the expression ( 11 1 + 12 2 + 13 3 + 14 4 + 15 5 + 16 6 ) is T...
CAT
Quantitative Ability
Theory of Numbers
Remainders
Properties of Remainders

64 
Find the last 2 digits of 123123! Type in your answer as an integer. For example, if your answer is...
CAT
Quantitative Ability
Theory of Numbers
Remainders

65 
Given two different prime numbers P and Q, which of the following is not true?
CAT
Quantitative Ability
Theory of Numbers
Factors, Multiples

66 
N is a natural number. How many values of N exist, such that N2 + 24N + 21 has exactly three fa...
CAT
Quantitative Ability
Theory of Numbers
Factors, Multiples

67 
Two numbers are in the ratio 17:13. If their HCF is 15, what is the sum of two numbers? Type in you...
CAT
Quantitative Ability
Theory of Numbers
Factors, Multiples
HCF, LCM

68 
The number of zeroes at the end of 1 99 × 2 98 × 3 97 ×..........× ...
CAT
Quantitative Ability
Theory of Numbers
Factors, Multiples
Numbers, Properties & Operations

69 
Find the gcd (111…11 hundred ones ; 11…11 sixty ones).
CAT
Quantitative Ability
Theory of Numbers
Factors, Multiples
HCF, LCM

70 
The number 11 and the quotient obtained by dividing a number 'n' by 121 are c...
CAT
Quantitative Ability
Theory of Numbers
Numbers, Properties & Operations

71 
Find the units digit of LCM of 13501 – 1 and 13501 + 1. Type in your answer as an integer. Fo...
CAT
Quantitative Ability
Theory of Numbers
Factors, Multiples
HCF, LCM

72 
Which of the following number can be obtained on rationalizing the given number ...
CAT
Quantitative Ability
Theory of Numbers
Numbers, Properties & Operations
Representation of Numbers
Classification of numbers

73 
Sum of two number x and y is 1050. What is the maximum value of the HCF between x and y? Type in yo...
CAT
Quantitative Ability
Theory of Numbers
Factors, Multiples
HCF, LCM

74 
An Army Commander wishing to draw up his 5180 men in the form of a solid square found that he had 4 ...
CAT
Quantitative Ability
Theory of Numbers
Factors, Multiples

75 
Find the number of ways in which 57 can be expressed as a product of 3 factors. Type in y...
CAT
Quantitative Ability
Theory of Numbers
Factors, Multiples

76 
What is the remainder when S = 1! + 2! + 3! +…….+ 19! + 20! is divided by 20? Type in...
CAT
Quantitative Ability
Theory of Numbers
Remainders

77 
Find the remainder when ( 300300  1 ) is divided by 1001. Type in your answer as an integer. ...
CAT
Quantitative Ability
Theory of Numbers
Remainders

78 
Find the sum of all the positive numbers less than or equal to 100, which are not factors ...
CAT
Quantitative Ability
Theory of Numbers
Factors, Multiples

79 
Find the remainder when (3324)7 is divided by 6. Type in your answer as an integer. For exampl...
CAT
Quantitative Ability
Theory of Numbers
Base System

80 
Find the last two digits of 78(379k+2), where k is a natural number Type in your answer as an integ...
CAT
Quantitative Ability
Theory of Numbers
Remainders

81 
What is the remainder when 33333...........333 (200 times) is divided by 13? Type in your answer as...
CAT
Quantitative Ability
Theory of Numbers
Remainders

82 
Find the remainder when 52k is divided by 13 where ( k = 1! + 2!+.......+ 5!). Type in y...
CAT
Quantitative Ability
Theory of Numbers
Remainders

83 
The square root of octal number 2000 is :
CAT
Quantitative Ability
Theory of Numbers
Base System

84 
The remainder when (888!) 999 169 is divided by 77 is : Type in your answer as an ...
CAT
Quantitative Ability
Theory of Numbers
Remainders

85 
How many ordered pairs of positive integers (x, y) exist such that HCF (x, y) + LCM (x, y) = 91? Ty...
CAT
Quantitative Ability
Theory of Numbers
Factors, Multiples
HCF, LCM

86 
The remainder when (1! + 2! + 3! + ….. + 50!) is divided by 10 is: Type in your answer as an...
CAT
Quantitative Ability
Theory of Numbers
Remainders

87 
What is the remainder when 1 + (11)11 + (111)111 + (1111)1111 + ...(111.(10 digits)..111)111…...
CAT
Quantitative Ability
Theory of Numbers
Remainders

88 
The remainder when (888222888222888222 …. upto 9235 digits) is divided by 53 is : ...
CAT
Quantitative Ability
Theory of Numbers
Remainders

89 
What is the remainder when the number 123123123.....123123(300 digits) is divided by 99? Type in yo...
CAT
Quantitative Ability
Theory of Numbers
Remainders

90 
If p is a prime number greater than 3 such that ( 8p + 1 ) is prime, , then ( &...
CAT
Quantitative Ability
Theory of Numbers
Numbers, Properties & Operations

91 
What is the sum of all twodigit numbers that give a remainder of 3 when they are divided by 7? Typ...
CAT
Quantitative Ability
Theory of Numbers
Remainders

92 
Find the remainder when (40! + 2) is divided by 41. Type in your answer as an integer. For example,...
CAT
Quantitative Ability
Theory of Numbers
Remainders
Advanced Theorems
Wilson's Theorem

93 
If n is a positive prime integer, what is the remainder when ( n2n1) is divided by ( n &...
CAT
Quantitative Ability
Theory of Numbers
Remainders

94 
In which of the following scale is the number 305 a perfect cube?
CAT
Quantitative Ability
Theory of Numbers
Base System

95 
The last two digit in the expansion of (1989)91 : Type in your answer as an integer. For example, ...
CAT
Quantitative Ability
Theory of Numbers
Remainders

96 
How many three digit numbers in base 11 are possible such that when they are expressed in base 9, ha...
CAT
Quantitative Ability
Theory of Numbers
Base System

97 
Find the total number of possible values of 'n' if n perfectly divides (3030)31 and is ...
CAT
Quantitative Ability
Theory of Numbers
Base System

98 
A palindromic number reads the same forward and backward. A palindromic number with even number of d...
CAT
Quantitative Ability
Theory of Numbers
Base System

99 
Find the least number which must be subtracted from 9269 so that resulting number is exactly divisib...
CAT
Quantitative Ability
Theory of Numbers
Remainders
Properties of Remainders

100 
What is the decimal equivalent to the hexadecimal number (1000.........(23 times zero)1)16? ...
CAT
Quantitative Ability
Theory of Numbers
Base System
