1	A two-digit 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 3-digit 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&nbsp... 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 two-digit 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 ( n2n-1) 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