This document contains 100 multiple choice questions related to number theory and mathematics. The questions cover topics such as divisibility rules, prime numbers, factorization, fractions, decimals, percentages, and algebraic expressions. Sample questions include finding the units digit when large numbers are multiplied, determining which number should replace an asterisk for a number to be divisible by a given value, and identifying the tenth term in a sequence.

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NUMBER THEORY PROBLEMS
Question: If a number consists of units digit as a and the ten’s digit as b, such a number is:
(a) b + a
(b) bx
(c) 10b + x
(d) 10a + b
Ans: (c)
Question: If a number consists of units digit as 6 and the ten’s digit as 5, such a number is:
(a) 65
(b) 56
(c) 605
(d) 506
Ans: (b)
Question: If n is even, n(n2
-1) is always divisible by :
(a) 6
(b) 8
(c) 15
(d) 17
Ans: (a)
Question: If n is odd, n(n2
-1) is always divisible by :
(a) 18
(b) 20
(c) 24
(d) 32
Ans: (c)
Question: If n is even number, then n(n2
+ 10) is always divisible by:
(a) 10
(b) 4
(c) 6
(d) 28
Ans: (b)
Question: 9876543210 is divisible by :
(a) 5, 9 and 11
(b) 5, 9 but not by 11
(c) 9 and 11 but not by 5
(d) 11 and 5 but not by 9
Ans : (b)
Question: If a four digit number 2AB5 ( A and B digits ) is divisible by 9, then the number AB is :
(a) 38
(b) 24
(a) 44
(b) 13

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Ans: (a)
Question: If the six digit number 4A52B6 is divisible by 2 as well as 3, then the number AB is :
(a) 22
(b) 21
(a) 20
(b) 12
Ans: (a)
Question: For any natural number n(52n+2
– 24 n – 25) is divisible by :
(a) 25
(b) 50
(c) 510
(d) 576
Ans: (d)
Question: If a number is divisible by 6 and 9 both, then it is necessarily divisible by :
(a) 54
(b) 18
(a) 12
(b) 27
Question: If a number is divisible by 2 and 3 both, then it is necessarily divisible by :
(a) 6
(b) 8
(a) 9
(b) 12
Ans : (a)
Question: The HCF and the LCM of a pair of numbers are 11 and 847 respectively. How many such
distinct pairs are possible?
(a) 3
(b) 1
(c) 2
(d) 4
Ans: (c)
Question: H.C.F of 96 and 108 is
(a) 4
(b) 6
(c) 12
(d) 3
Ans :(c)
Question: If the product of two numbers is 256 and their HCF is 4, then their LCM will be :
(a) 64
(b) 128
(c) 84
(d) None of these
Ans : (a)
Question: If the LCM and HCF of two numbers is 54 and 4 respectively, then the product of two
numbers will be:
(a) 315

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(b) 216
(a) 457
(b) 228
Ans : (b)
Question: If the LCM and HCF of two numbers is 324 and 3 respectively, If the one number is 12 then
other number will be :
(a) 91
(b) 82
(c) 81
(d) 80
Ans: (c)
Question: The smallest whole number by which 79633125 must be multiplied for the product to be a
perfect square is :
(a) 11
(b) 5
(a) 13
(b) 3
Ans: (c)
Question: The next number in the sequence 1/22,4/25, 9/28, 16/31, 25/34, is
(a) 28/35
(b) 30/37
(a) 36/37
(b) 36/35
Ans: (c)
Question: The next number in the sequence 4/41, 5/51, 6/61, 7/71, is
(a) 8/81
(b) 9/81
(a) 8/75
(b) 8/78
Ans: (a)
Question: The number of terms in the sequence 5, 9, 13, …………….189 is
(a) 45
(b) 46
(a) 48
(b) 47
Ans: (d)
Question: The number of terms in the sequence 2, 9, 16,23 …………….338 is
(a) 48
(b) 46
(a) 49
(b) 45
Ans: (c)
Question: If a
3 27 , then the value of a is:
(a) 4
(b) 6

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(c) 8
(d) 12
Ans: (b)
Question: If
n
5 625
, then the value of n is:
(a) 8
(b) 10
(c) 11
(d) 12
Ans: (a)
Question: What is the least number which when divided by 26, 34, 47, 58, and 112 leaves the remainder
16, 24, 37,48, and 102 respectively
(a) 53282246
(b) 53582246
(c) 55326485
(d) 58565452
Ans : (a)
Question: What is the least number which when divided by 16, 20, 32, 42, and 50 leaves the remainder
12, 16, 28,38, and 46 respectively
(a) 11396
(b) 10396
(c) 10256
(d) 12546
Ans: (b)
Question: The least multiple of 7 which leaves a remainder 3 when divided by 4 or 12 or 16 is :
(a) 147
(b) 195
(c) 168
(d) 140
Ans: (a)
Question: The least multiple of 5 which leaves a remainder 5 when divided by 6 or 10 or 15 is :
(a) 152
(b) 153
(c) 152
(d) 155
Ans : (d)
Question: The least multiple of 9 which leaves a remainder 7 when divided by 9 or 13 or 15 is :
(a) 4102
(b) 4212
(c) 4302
(d) 4402

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Ans: (a)
Question: The value
   
8
3 8 5 4 2 2
13
   
        
   
is
(a) 68/17
(b) 17/13
(c) 13/17
(d) 13/68
Ans: (c)
Question: The value
      3 6 5 3 2 2 2       
is
(a) 4
(b) 3
(c) 2
(d) 0
Ans: (a)
Question: The value of
3.6 3.6 3.6 2.4 2.4 2.4
3.6 3.6 3.6 2.4 2.4 2.4
    
     is
(a) 0.54
(b) 0.56
(c) 0.94
(d) 1.25
Ans : (a)
Question: The value of
1
1
1
1
1
1
9



is:
(a) 29/10
(b) 29/19
(c) 10/29
(d) 10/19
Ans: (b)
Question: The value of
4
4
4
4
4
4
7



is:
(a) 376/188
(b) 188/36
(c) 188/39
(d) 188/9
Ans: (c)
Question: The tenth term of 8, 15, 22, 29,………..
(a) 81

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(b) 71
(c) 51
(d) 91
Ans: (b)
Question: The seventh term of 112, 140, 168, …………..
(a) 270
(b) 250
(c) 280
(d) 300
Ans: (c)
Question: P and Q are only two odd numbers with P > Q. The largest even integer which divides P2
-Q2
is :
(a) 2
(b) 8
(c) 4
(d) 6
Ans: (b)
Question: M and N are only two even numbers with M > N. The largest even integer which divides M2
-
N2
is :
(a) 2
(b) 4
(c) 8
(d) 10
Ans: (d)
Question: There are four prime numbers written in ascending order of magnitude. If the product of the
first three is 105 and the last three is 385, then the first number is:
(a) 2
(b) 5
(c) 7
(d) 3
Ans: (d)
Question: There are four composite numbers written in ascending order of magnitude. If the product of
the first three is 192 and the last three is 432, then the first number is:
(a) 4
(b) 6
(c) 2
(d) 8
Ans: (a)
Question: If (2158) 258
is multiplied out, the units’ digit in the product is:
(a) 3
(b) 5
(c) 6
(d) 4
Ans: (d)
Question: If (21567)125
is multiplied out, the units’ digit in the product is :
(a) 1

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(b) 7
(c) 5
(d) 3
Ans : (b)
Question: If (874516)145689
is multiplied out, the units’ digit in the product :
(a) 4
(b) 3
(c) 6
(d) 1
Ans: (c)
Question: The square root of
0.324 0.081 4.624
1.5625 0.0289 72.9 64
 
   is:
(a) 0.24
(b) 0.024
(c) 2.40
(d) 24.0
Ans: (b)
Question: The square root of
0.126 0.064 6.624
1.6625 0.0189 82.9 49
 
   is:
(a) 0.020
(b) 20.02
(c) 4.02
(d) 3.02
Ans: (a)
Question: If 20164 142 , then the value of 20164 201.64 2.0164  is :
(a) 157.47
(b) 157.62
(c) 156.98
(d) 157.54
Ans: (b)
Question: If 205209 453 , then the value of 2052.09 20.5209 0.205209  is :
(a) 50.24
(b) 50.21
(c) 457.75
(d) 50.28
Ans: (d)
Question: If 15 3x

, then the value of x is
(a) 2
(b) 3
(c) 1
(d) 0
Ans: (b)
Question: The value of 0.6666… is

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(a)
9
6
(b)
99
66
(c)
999
666
(d)
9999
6666
Ans: (a)
Question: If 12/124
)x(49  , then value of x is
(a) 12
(b) 7
(c) 24
(d) 4
Ans: (b)
Question: The value of x, when 2x+4
. 3x+1
= 288
(a) 1
(b) –1
(c) 0
(d) None of these
Ans: (a)
Question: If a number, of two digits, is 2 times the sum of its digits, the number formed by interchange
the digits is equal to sum of the digits multiplied by :
(a) 1
(b) 8
(c) 9
(d) 4
Ans:(c)
Question: The value of
2 2 2 2
2
2 4 2 4 8 2 4 8 16 2 4 8 16 32
   
         
upto four places of decimal
is :
(a) 2.2833
(b) 2.2598
(c) 2.2832
(d) 2.5636
Ans: (c)
Question: If
x 14
1
169 13
 
, then x equals :
(a) 0
(b) 14
(c) 27
(d) 15
Ans: (c)

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Question: If
x 18
1
225 15
 
, then x equals :
(a) 89
(b) 99
(c) 100
(d) 145
Ans: (b)
Question: The expression
 136
1 1
1
6 4 

 equals :
(a)
24
10
(b)
10
24
(c)
24
15
(d)
15
24
Ans : (a)
Question: The expression
 140
1 1
1
5 3 

 equals :
(a)
132
15
(b)
15
8
(c)
8
15
(d)
15
11
Ans : (b)
Question: The value of 3 up to three places of decimals is :
(a) 1.734
(b) 1.730
(c) 1.732
(d) 1.735
Ans: (c)
Question: The value of 5 up to four places of decimals is :
(a) 2.2360
(b) 2.2370
(c) 2.2365
(d) 2.2361
Ans: (a)

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Question: If the number 42573* is completely divisible by 72, then which number should replace the
asterick(*)?
(a) 9
(b) 5
(c) 7
(d) 6
Ans: (d)
Question: If the number 82563* is completely divisible by 60, then which number should replace the
asterick(*)?
(a) 0
(b) 2
(c) 3
(d) 1
Ans: (a)
Question: The largest number, which on dividing by 25, 73, and 97 leaves equal remainder in each case ,
is :
(a) 6
(b) 21
(c) 23
(d) 24
Ans: (d)
Question: The largest number, which on dividing by 27, 77, and 202 leaves equal remainder in each case,
is :
(a) 7
(b) 8
(c) 25
(d) 23
Ans (c)
Question: If 3 3 4 5/2 a 4
3 3 3 
   , then the value of a is :
(a) 3
(b) 4
(c) 5
(d) 2
Ans :(d)
Question:
n 4 n
3
n 3
2 2(2 )
2
2.(2 )





is equal to :
(a) 2n+1
(b) 0
(c) 1
(d) 2n+3
Ans: (c)
Question: 4.888  0.065 is equal to :
(a) 70.2
(b) 65.2
(c) 75.2

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(d) 85.2
Ans: (c)
Question: The value of 0.67 is :
(a)
61
90
(b)
64
90
(c)
61
99
(d)
67
90
Ans: (a)
Question: The sum of 2.75 and3.78 is :
(a) 5.53
(b) 6.53
(c) 1.53
(d) 4.53
Ans: (d)
Question: The traffic lights at 3 different road crossings change after every 48 seconds, 72 seconds and
108 seconds respectively. If they change simultaneously at 7 a.m. then the next change will appear after
(a) 7 m 14 sec
(b) 7 m 16 sec
(c) 7m 12 sec
(d) 7 m 18 sec
Ans: (c)
Question: If 3th
power of 9 is subtracted from 6
th
power of 2, then the digit in 10s place is
(a) 6
(b) 8
(c) 9
(d) 7
Ans: (c)
Question: The product of and is
(a) 124
(b) 134
(c) 144
(d) 154
Ans: (c)
Question: The H.C.F. of two numbers is 14 and their L.C.M. is 11592. If one of the number is 504, find
the other.
(a) 324
(b) 322
64 243

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(c) 325
(d) 328
Ans : (b)
Question: The product of two numbers is 18850 and their L.C.M. is 754. Find their H.C.F.
(a) 15
(b) 20
(c) 28
(d) 25
Ans: (d)
Question: Find the least number which when divided by 6, 9, 12, 15, and 18 leaves the same remainder 2
in each case.
(a) 184
(b) 185
(c) 182
(d) 135
Ans: (c)
Question:
7 5
7 5

 is equal to :
(a) 6 + 35
(b) 6 - 35
(c) 2
(d) 0
Ans: (a)
Question:
7 3
7 3

 is equal to :
(a)
5 21
4

(b)
5 21
2

(c) 0
(d) 1
Ans: (b)
Question: If a and b are two digits of the number 625ab such that this number is divisible by 80, then (a +
b) is equal to :
(a) 6
(b) 4
(c) 2
(d) 3
Ans: (a)
Question: The largest natural number which exactly divides the product of any four consecutive natural
numbers, is :
(a) 6
(b) 24

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(c) 120
(d) 12
Ans: (c)
Question: The value of 98
1
...
43
1
32
1
21
1






 is
(a) 1
(b) 2
(c) 4
(d) 8
Ans: (b)
Question: If a = 2 + 3 and b = 2 - 3 then 2 2
1 1
a b
 is equal to
(a) 14
(b) -14
(c) 8 3
(d) 8 3
Ans: (d)
Question:
0
1
64
 
 
 
+ (64)-1/2
- (-32)4/5
is equal to
(a) -15
7
8
(b)
1
16
8
(c)
7
14
8

(d)
1
17
8
Ans: (c)
Question: The smallest number which must be added to 803642 in order to obtain a multiple of 9 is
(a) 3
(b) 4
(c) 5
(d) 6
Ans: (b)
Question: Find the total number of prime numbers lying between 120 and 140.
(a) 3
(b) 4
(c) 5
(d) 6
Ans: (b)
Question: If a and b are whole numbers such that ab
= 169. The value of (a-3)b-1
is :
(a) 1
(b) 169

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(c) 13
(d) 10
Ans: (d)
Question: A number when divided by 136 leaves 36 as remainder. If the same number is divided by 17,
what will be the remainder:
(a) 2
(b) 3
(c) 5
(d) 15
Ans: (a)
Question: The least number which leaves remainders 2, 3, 4, 5 and 6 on dividing by 3, 4, 5, 6 and 7
respectively, is:
(a) 412
(b) 419
(c) 421
(d) 426
Ans: (b)
Question: A sum of Rs. 9.00 is made up of 90 coins which are either 20 Paise or 5 Paise coins. The
number of 5 Paise coins are ?
(a) 60
(b) 50
(c) 40
(d) 30
Ans: (a)
Question: A number when successively divided by 2, 5, 9 leaves 2, 3 and 4 as remainders respectively. If
the number be divided by 9, 5 and 2 respectively, the respective remainders will be :
(a) 4,3,2
(b) 3, 4, 2
(c) 2, 4, 3
(d) 4, 2, 3
Ans: (a)
Question: If the square of a number of two digits is subtracted from the square of the number formed by
interchanging the digits, the largest number by which the result is always divisible is :
(a) 9
(b) 99
(c) 11
(d) 15
Ans: (b)
Question: The largest natural number by which the product of three consecutive odd numbers is always
divisible is :
(a) 10
(b) 15
(c) 25
(d) 35
Ans: (b)

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Question: If 7 2.64 , then the value of
3 7
2 7 0.28
will be :
(a) 1.564
(b) 1.584
(c) 15.84
(d) 158.4
Ans: (b)
Question: A four digit number divisible by 7 becomes divisible by 3 when 10 is added to it. The largest
such number is :
(a) 9987
(b) 9989
(c) 9947
(d) 9996
Ans: (d)
Question: How many numbers between 200 and 300 begin with or end with a digit 5 ?
(a) 10
(b) 20
(c) 15
(d) 35
Ans: (b)
Question: The least perfect square, which is divisible by each of 21, 36 and 66 is
(a) 214344
(b) 214434
(c) 213444
(a) 231444
Ans (c)
Question: Which of the following is divisible by 9?
(a) 1278
(b) 1754
(c) 1779
(d) 1770
Ans (a)