Number System
1. The smallest number of five digits exactly
divisible by 476 is
(1) 47600 (2) 10000 (3) 10476 (4)
10472 (5) None of these
2. The greatest among the following numbers 
, 
, 1, 
, , 1,
(1) 
(2)
(3)
(4) (5) None of these
(2)
(3)
(4) (5) None of these
3. When 335 is added to 5A7, the result is
8B2. 8B2 is divisible by 3. What is the
largest possible value of A ?
(1) 8 (2) 2 (3) 1 (4)
4 (5) None of these
4. Sum of three fractions is 2
. On dividing the largest fraction by the smallest fraction, 
is obtained which is 
greater than the middle fraction.
The smallest fraction is
. On dividing the largest fraction by the smallest fraction, is obtained which is greater than the middle fraction.
The smallest fraction is
(1) 
(2) 
(3) 
(4) 
(5) None of these
(2) (3) (4) (5) None of these
5. A number when divided by 899 gives a
remainder 63. If the same number is divided by 29, the remainder will be :
(1) 10 (2) 5 (3) 4 (4) 2 (5) None of these
6. A six digit number is formed by repeating
a three digit number for example, 256, 256 or 678, 678 etc. Any number of this
form is always exactly divisible by :
(1) 7
only (2) 11 only (3) 13 only (4) 1001 (5) None
of these
7. The smallest number to be added to 1000, so
that 45 divided the sum exactly :
(1) 35 (2) 80 (3) 20 (4) 10 (5) None of these
8. Which of the following numbers will always
divide a six-digit number of the form xyxyxy (where 1≤x≤9, 1≤y≤9) ?
(1) 1010 (2) 10101 (3) 11011 (4) 11010 (5) None of these
9. The divisor is 25 times the quotient and 5
times the remainder. If the quotient is 16. The dividend is
(1) 6400 (2) 6480 (3) 400
(4) 480 (5) None of these
10. The product of two positive numbers is
11520 and their quotient is
. Find the difference of two numbers
. Find the difference of two numbers
(1) 60 (2) 64 (3) 74 (4) 70 (5) None of these
11. A student was asked to multiply a number
by 
. His result was 10 less than the correct answer. The number was :
. His result was 10 less than the correct answer. The number was :
(1) 10 (2) 12 (3) 15 (4) 20 (5) None of these
12. If 
of the difference of 2
and 1
is subtracted from of 3 the result is
of the difference of 2 and 1 is subtracted from of 3 the result is
(1) 
(2) 
(3)
(4) 
(5) None of
these
(2) (3)
(4) (5) None of
these
13. A number when divided successively by 4
and 5 leaves remainder 1 and 4 respectively. When it is successively divided by
5 and 4 the respective remainders will be
(1) 4, 1 (2) 3, 2 (3)
2, 3 (4) 1, 2 (5) None of these
14. Each member of a picnic party contributed
twice as many rupees as the total number of members and the total collection
was Rs. 3042. The number of members present in the party was
(1) 2 (2)
32 (3)
40 (4) 39 (5) None of these
15. How many natural numbers divisible by 7 are
there between 3 and 200 ?
(1) 27 (2) 28 (3) 29 (4) 36 (5) None of these
16. The sum of first sixty numbers from one to
sixty is divisible by
(1) 13 (2) 59 (3) 60 (4) 61 (5) None of these
17. A number when divided by 3 leaves a
remainder 1. When the quotient is divided by 2, it leaves a remainder 1. What
will be the remainder when the number is divided by 6 ?
(1) 3 (2) 4 (3) 5 (4) 2 (5) None of these
18. The product of two numbers is 9375 and the
quotient, when the larger one is divided by the smaller, is 15. The sum of the
number is :
(1) 395 (2) 380 (3) 400 (4) 425 (5) None of these
19. (719 + 2) is divided by 6, the
remainder is :
(1) 5 (2) 3 (3) 2 (4) 1 (5) None of these
20. 64329 is divided by a certain number.
While dividing, the numbers, 175, 114 and 213 appear as three successive
remainders. The divisor is
(1) 184 (2) 224 (3) 234 (4) 296 (5) None of these
21. A number consists of two digits ,if the
number formed by interchanging the digits is added to the original number, the
resulting number (i.e. the sum) must be divisible by
(1) 11 (2) 9 (3) 5 (4) 3 (5) None of these
22. A number when divided by 5 leaves a
remainder 3. What is the remainder when the square of the same number is
divided by 5
(1) 1 (2) 2 (3)
3 (4) 4 (5) None of these
23. The remainder when 321 is
divided by 5 is
(1) 1 (2) 2 (3) 3 (4)
4 (5)
None of these
24. A student was asked to divide a number by
6 and add 12 to the quotient. He, however, first added 12 to the number and
then divided it by 6, getting 112 as the answer. The correct answer should have
been
(1) 124 (2)
122 (3) 118 (4) 114 (5) None of these
25. The expression 26n – 42n,
where n is a natural number is always divisible by
(1) 15 (2) 18 (3) 36 (4) 48 (5) None of these
26. (461 + 462 + 463)
is divisible by
(1) 3 (2) 11 (3) 13 (4) 17 (5) None of these
27. 47 is added to the product of 71 and an
unknown number. The new number is divisible by 7 giving the quotient 98. The
unknown number is a multiple of
(1) 2 (2)
5 (3) 7 (4) 3 (5) None of these
28. The number of integers in between 100 and
600, which are divisible by 4 and 6 both, is
(1) 40 (2) 42 (3) 41 (4) 50 (5) None of these
29. If the number formed by the last two
digits of a three digit integer is an integral multiple of 6, the original
integer itself will always be divisible by
(1) 6 (2) 3 (3) 2 (4) 12 (5) None of these
30. Divide 37 into two parts so that 5 times
one part and 11 times the other are together 227
(1) 15,
22 (2) 20, 17 (3) 25, 12 (4) 30,
7 (5) None
of these
31. Two numbers 11284 and 7655, when divided
by a certain number of three digits, leaves the same remainder. The sum of
digits of such a three-digit number is
(1) 8 (2) 9 (3)
10 (4) 11 (5) None
of these
32. The smallest number that must be added to
803642 in order to obtain a multiple of 11 is
(1) 1 (2)
4 (3) 7 (4) 9 (5) None
of these
33. If [n] denotes the greatest integer < n
and (n) denotes the smallest integer ˃ n, where n is any real number, then
(1
) 
[1] – (1) 
[1] + (1.5)
) [1] – (1) [1] + (1.5)
(1) 1.5 (2) 2 (3) 2.5 (4) 3.5 (5) None of these
34. 999
999 =
999 =
(1) 998999 (2) 999899 (3) 989999 (4) 999989 (5) None of these
35. The value of 
is closest to
is closest to
(1) 0.002 (2) 0.02 (3) 0.2 (4) 2 (5)
None of these
36. 
+ (999
) 99 is equal to
+ (999) 99 is equal to
(1) 1 (2) 99000 (3) 99800 (4) 99900 (5) None of these
37. If m and n are positive integers and (m -
n) is an even number, then (m2 – n2) will be always
divisible by
(1) 4 (2) 6 (3) 8 (4) 12 (5) None of these
38. If 5432*7 is divisible by 9, then the
digit in place of * is :
(1) 0 (2)
1 (3) 6 (4) 9 (5) None of these
39. How many 3-digit numbers, in all, are
divisible by 6 ?
(1) 140 (2)
150 (3)
160 (4) 170 (5) None of these
40. If n is an integer, then (n3 -
n) is always divisible by
(1) 4 (2) 5 (3) 6 (4) 7 (5) None of these
41. If the sum of the digits of any integer
lying between 100 and 1000 is subtracted from the number, the result always is
(1) divisible
by 6 (2) divisible by 2 (3) divisible
by 9 (4) divisible by 5 (5) None of these
42. If a number is divisible by both 11 and
13, then it must be necessarily
(1) divisible
by (11 + 13)
(2) divisible
by (13 - 11)
(3) divisible
by (11 13)
13)
(4) 429 (5) None of these
43. Both the end digits of a 99 digit number N
are 2. N is divisible by 11, then all the middle digits are
(1) 1 (2) 2
(3) 3 (4) 4 (5) None of these
44. A 4-digit number is formed by repeating a
2-digit number such as 2525, 3232, etc. Any number of this form is always
exactly divisible by
(1) 7 (2) 11 (3) 13
(4) smallest 3-digit prime number (5) None
of these
45. The greatest whole number, by which the
expression n4 + 6n3 + 11n2 + 6n + 24 is
divisible for every natural number n, is
(1) 6 (2) 24 (3) 12 (4) 48 (5) None of these
46. What least number, of 5 digits is
divisible by 41 ?
(1) 10045 (2) 10004 (3) 10041 (4) 41000 (5)
None of these
47. Find the largest number, which exactly
divides every number of the form (n3 - n)(n - 2) where n is a
natural number greater than 2
(1) 6 (2) 12 (3) 24 (4) 48 (5) None of these
48. The solution to the inequality 12x – 61 ≤
6 is
(1) x ≤ 6 (2) 0
≤ x ≤ 6 (3) -6 ≤ x ≤ 6 (4) -6 ≤ x ≤ 0 (5) None of these
49. The product of all the prime numbers
between 80 and 90 is
(1) 83 (2) 89
(3) 7387 (4) 598347 (5) None
of these
50. The maximum value of F in the following
equation
5E9 + 2F8 +
3G7 = 1114 is where E, F, G each stands for any digit.
(1) 8 (2) 9 (3) 7 (4) 5 (5) None of these
51. The sum of four numbers is 48. When 5 and
1 are added to the first two; and 3 and 7 are subtracted from the 3rd
and 4th , the numbers will be equal. The numbers are
(1) 9, 7, 15,
17 (2) 4, 12, 12, 20 (3) 5, 11, 13, 19 (4) 6,10, 14, 18 (5)
None of these
52. The difference between the greatest and
the least four digit numbers that least four digit numbers begin with 3 and
ends with 5 is
(1) 999 (2) 900 (3) 990
(4) 909 (5) None of these
53. A runner 1 laps of a 5 lap race. What
fractional part of the race remains to be run?
laps of a 5 lap race. What
fractional part of the race remains to be run?
(1) 
(2) 
(3) (4) 
(5) None of these
(2) (3) (4) (5) None of these
54. A boy on being asked what 
of a certain fraction was, made
the mistake of dividing the fraction by and so got an answer which
exceeded the correct answer by 
. Find the fraction
of a certain fraction was, made
the mistake of dividing the fraction by and so got an answer which
exceeded the correct answer by . Find the fraction
(1) (2) 
(3) (4) 
(5) None of these
(2) (3) (4) (5) None of these
55. The number 2.52, when written as a
fraction and reduced to lowest terms, the sum of the numerator and denominator is
(1) 7 (2) 29 (3) 141 (4) 349 (5) None of these
56. 
of a rod is coloured red, 
orange, 
yellow, 
green, 
blue, 
black and the rest is violet. If
the length of the violet portion of the rod is 12.08 metres, then the length of
the rod is
of a rod is coloured red, orange, yellow, green, blue, black and the rest is violet. If
the length of the violet portion of the rod is 12.08 metres, then the length of
the rod is
(1) 16 m (2) 18 m
(3) 20 m (4) 30 m
(5) None of these
57. How many 
of together make 41 ?
of together make 41 ?
(1) 125 (2) 150 (3) 250 (4) 350 (5) None of these
58. A fraction having denominator 30 and lying
between and 
is
and is
(1) 
(2)
(3) 
(4) 
(5) None of these
(2)
(3) (4) (5) None of these
59. The sum of the numerator and denominator
of a positive fraction is 11. If 2 is added to both, the fraction is increased
by 
. The difference of numerator and denominator of the fraction is
. The difference of numerator and denominator of the fraction is
(1) 5 (2) 3 (3) 1 (4) 9
(5) None of these
60. The denominator of a fraction is 3 more
than its numerator. If the numerator is increased by 7 and the denominator is
decreased by 2, we obtain 2. The sum of numerator and denominator of the
fraction is
(1) 5 (2) 13 (3) 17 (4) 19 (5) None of these
61. In an office, there are 108 tables and 132
chairs. If of the tables and of the chairs are broken. How
many people can work in the office if each person requires one table and one
chair ?
of the tables and of the chairs are broken. How
many people can work in the office if each person requires one table and one
chair ?
(1) 86 (2)
90 (3) 92 (4) 99 (5)
None of these
62. In a school of the boys are same in number as
of the girls and of the girls are same in number
as of the boys. The ratio of the
boys to girls in that school is
of the boys are same in number as
of the girls and of the girls are same in number
as of the boys. The ratio of the
boys to girls in that school is
(1) 2 : 1 (2) 5
: 2 (3) 4 : 3 (4) 3 : 2 (5) None of these
63. In a class, there are ‘z’ students. Out of
them ‘x’ are boys. What part of the class is composed of girls?
(1) 
(2)
(3) 1 - (4) 
- 1 (5) None of these
(2)
(3) 1 - (4) - 1 (5) None of these
64. Divide 50 into two parts so that the sum
of their reciprocals is 
.
.
(1) 35,
15 (2) 20, 30 (3)
24, 36 (4) 28, 22
(5) None of these
65. The digit in unit’s place of the product
81 82 83 84 ……………. 89 is
82 83 84 ……………. 89 is
(1) 0 (2) 2 (3) 6 (4) 8 (5) None of these
66. 0.393939…………is equal to
(1) 
(2) 
(3) 
(4) 
(5) None of these
(2) (3) (4) (5) None of these
67. The digit in unit’s place of the product
(2153)167 is :
(1) 1 (2) 3 (3) 7 (4) 9 (5) None of these
68. The last digit of 340 is
(1) 1 (2) 3 (3) 7 (4) 9 (5) None of these
69. Ina two digit number, the digit at the
unit’s place is 1 less than twice the digit at the ten’s place. If the digits
at unit’s and ten’s place are interchanged, the difference between the new and
the original number is less than the original number by 20. The original number
is
(1) 59 (2) 23 (3) 35 (4) 47 (5) None of these
70. By interchanging the digits of a two digit number we get a number which is four times
the original number minus 24. If the unit’s digit of the original number
exceeds its ten’s digit by 7, then original number is
(1) 29 (2) 36 (3) 58 (4) 18 (5) None of these
71. The sum of three consecutive odd natural
numbers is 147. Then, the middle number is :
(1) 47 (2) 48 (3) 49 (4) 51 (5) None of these
72. The sum of first 20 odd natural numbers is
equal to :
(1) 210 (2) 300 (3) 400 (4) 420 (5)
None of these
73. The sum of all natural numbers from 75 to
97 :
(1) 1598 (2) 1798 (3)
1958 (4) 1978 (5)
None of these
74. The sum of all natural numbers between 100
and 200 which are multiples of 3 is :
(1) 5000 (2) 4950 (3) 4980 (4) 4900 (5)
None of these
75. The sum of the squares of three
consecutive natural numbers is 2030. Then, what is the middle number
(1) 25 (2) 26 (3) 27 (4) 28 (5) None of these
76. What is the sum of two consecutive even
numbers, the difference of whose square is 84 ?
(1) 38 (2) 34 (3) 42 (4) 46 (5) None of these
77. The sum of all the natural numbers from 51
to 100 is
(1) 5050 (2)
4275 (3) 4025 (4) 3775 (5) None of these
78. The sum of all the 2-digit numbers is
(1) 4995 (2) 4950 (3) 4945 (4) 4905 (5) None of these
79. The sum of all the 3-digit numbers, each
of which on division by 5 leaves remainder 3, is
(1) 180 (2) 1550 (3) 6995 (4) 99090 (5) None of these
80. Out of six consecutive natural numbers, if
the sum of first three is 27, what is the sum of the other three ?
(1) 36 (2) 35 (3) 25 (4) 24 (5) None of these
81. Which one of the following is a factor of
the sum of first twenty five natural numbers ?
(1) 26 (2) 24 (3) 13 (4) 12 (5) None of these
82. The sum of all even between 21 and 51 is
(1) 518 (2)
540 (3) 560 (4) 596 (5) None of these
83. If the sum of five consecutive integers is
S, then the largest of those integers in terms of S is
(1) 
(2)
(3)
(4) 
(5)
None of these
(2)
(3)
(4) (5)
None of these
84. The sum of all those prime numbers which
are not greater than 17 is
(1) 59 (2) 58 (3) 41 (4) 42 (5)
None of these
85. The sum of the squares of 3 consecutive
positive numbers is 365. The sum of the numbers is
(1) 30 (2) 33 (3)
36 (4) 45 (5) None of these
86. Find the sum of all positive multiples of
3 less than 50
(1) 400 (2) 404 (3) 408 (4) 412 (5) None
of these
87. What is the arithmetic mean of first 20
odd natural numbers
(1) 19 (2) 17 (3) 22 (4) 20 (5) None of these
88. Two positive whole numbers are such that
the sum of the first number and twice the second number is 8 and their
difference is 2. The numbers are :
(1) 7.5 (2) 6.4 (3) 4.2 (4) 3.5 (5) None
of these
89. Given that 0.111…….=
; 0.444 =
; 0.444 =
(1) 
(2)
(3)
(4) 
(5) None of these
(2)
(3)
(4) (5) None of these
90. Numbers 2, 4, 6, 8, 10,………196, 198, 200
are multiplied together. The number of zeros at the end of the product on the
right will be equal to
(1) 21 (2) 22 (3) 24 (4) 25 (5) None of these
91. 800 chocolates were distributed among the
students of a class. Each student got twice as many chocolates as the number of
students in the class. The number of students in the class was
(1) 25 (2)
30 (3) 35 (4) 20 (5)
None of these
92. How many digits in all are required to
write numbers from 1 to 50 ?
(1) 100 (2) 92 (3) 91 (4) 50 (5) None of these
93. A number of friends decided to go on a
picnic and planned to spend Rs. 108 on eatables. Three of them however did not
turn up. As a consequence each one of the remaining had to contribute Rs. 3
extra. The number of them who attended the picnic was
(1) 15 (2) 12 (3) 9 (4) 6 (5) None of these
94. (99
+ 99
+ 99 + 99
+ 99
+ 99
) =
+ 99 + 99 + 99 + 99 + 99) =
(1) 603 (2) 600 (3)
598 (4) 597 (5)
None of these
95. 380 mangoes are distributed among some
boys and girls who are 85 in number. Each boy gets four mangoes and each girl
gets five. The number of boys is
(1) 25 (2) 125
(3) 225 (4) 250 (5) None of these
96. In a two digit number if it is known that
its units digit exceeds its tens digit by 2 and that the product of the given
number and the sum of its digits is equal to 144, then the number is
(1) 46 (2) 42 (3) 26 (4) 24 (5) None of these
97. A number of boys raised Rs. 400 for a
famine relief fund, each boy giving as many 25 paise coins as there were boys.
The number of boys was
(1) 40 (2) 16 (3) 20 (4)
100 (5) None of
these
98. Thrice the square of a natural number
decreased by four times the number is equal to 50 more than the number. The
number is
(1) 4 (2) 5 (3) 10 (4) 6 (5) None of these
99. The sum of the digits of a two digit
number is 10. The number formed by reversing the digits is 18 less than the
original number. Find the original number
(1) 81 (2) 46 (3)
64 (4) 60 (5) None of these
100.
I multiplied a natural number by 18 and another by 21 and added the
products. Which one of the following could be the sum
(1) 2007 (2) 2008 (3) 2006 (4) 2002 (5) None of these
101. In an examination, a student scores 4
marks for every correct answer and loses 1 mark for every wrong answer. If he
attempts all 75 questions and secures 125 marks, the number of questions he
attempts correctly is
(1) 35 (2) 40 (3) 42 (4) 46 (5) None of these
102. A man ate 100 grapes in 5 days. Each day,
he ate 6 more grapes than those he ate on the earlier day. How many grapes did
he eat on the first day
(1) 8 (2) 12 (3) 54
(4) 76 (5) None of these
103. A man has some hens and cows. If the
number of heads : number of feet = 12 : 35, find out the number of hens, if the
number of heads alone is 48.
(1) 28 (2) 26 (3) 24 (4) 22 (5) None of these
104. There are 50 boxes and 50 persons. Person
1 keeps 1 marble in every box. Person 2 keeps 2 marbles in every 2nd
box, person 3 keeps 3 marbles in every third box. This process goes on till
person 50 keeps 50 marbles in the 50th box. Find the total number of
marbles kept in the 50th box.
(1) 43 (2) 78 (3) 6 (4) 93 (5) None of these
105. 252 m of pant cloth and 141 m of shirt
cloth are available in a cloth store. To stitch one pant and one shirt, 2
m and 1 m of cloth are needed
respectively. Then the approximate number of pants and shirts that can be made
out of it are
m and 1 m of cloth are needed
respectively. Then the approximate number of pants and shirts that can be made
out of it are
(1) 80,
100 (2) 100,
80 (3) 100,
90 (4) 90, 80 (5) None of these
106.
The number 323 has
(1) three prime
factors (2) five prime factors (3) two prime factors
(4) no prime
factors (5) None of these
107. A and B have together three times what
Band C have, while A, B and C together have thirty rupees more than that of A.
If B has 5 times that of C, then A has
(1) Rs.
60 (2) Rs. 65 (3) Rs.
75 (4) Rs. 45 (5)
None of these
108. In a factory one out of every 9 is a
female worker. If the number of female workers is 125, the total number of
workers is
(1) 1250 (2) 1125 (3) 1025 (4) 1000 (5) None of these
109. A man engaged a servant on the condition
that he would pay hi Rs. 90 and a turban after service of one year. He served
only for nine months and received the turban and an amount of Rs. 65. The price
of turban is
(1) Rs. 25 (2) Rs. 18.75 (3) Rs. 10 (4) Rs. 2.50 (5)
None of these
110. If a certain number of two digits is
divided by the sum of its digits, the quotient is 6 and the remainder is 3. If
the digits are reversed and the resulting number is divided by the sum of the
digits, the quotient is 4 and the remainder is 9. The sum of the digits of the
number is
(1) 6 (2) 9 (3) 12 (4) 4
(5) None of these
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