Practice
1 A number when divided by 77 gives the quotient 40 and remainder one-eighth of the quotient . The number is
A.3855 B.2315 C.1545 D.3085
2 The numerator and denominator of a fraction are in the ratio 2:3 . If 6 is subtracted from the numerator the result will be 2/3 of the original fraction. What is the value of the numerator?
A.27 B.18 C.36 D.6
3 If the places of unit's and ten's digit of a three-digit number are interchanged , a new number greater than the original 5 If the places of unit's and ten's digit of a three-digit number are interchanged , a new number greater than the original number by 27 is obtained. Find the difference between the last two digits of that number?
A.3 B.6 C.9 D.Cannot be determined
4 Find the least number which is multiple of 3 and when divided by 20, 25, 35 and 40 leaves remainders 13, 18, 28, 33 respectively?
A.1393 B.4293 C.2793 D.None of these
5 The HCF of two numbers is 11 and their LCM is 693. If their sum is 176.Find the numbers?
A.11, 99 B.77,99 C.66,110 D.None of these
6 What is the HCF of 1/5, 2/7 , 3/11?
A.1/385 B.6 C.1/35 D.5/77
7 If x/y is 2/3, then the value of 4/5 + y-x/y+x is
A.0 B.1 C.2 D.5
8 When 0.165656565..... is converted into fraction, the result is
A.164/445 B.82/990 C.82/495 D.None of these
9 Find the greatest number less than 100000 which is divisible by 38, 60, 64 ?
A.98000 B.85000 C.76000 D.91200
10 Find the smallest number which when divided by 34 and 51 leaves the same remainder 20?
A.122 B.102 C.105 D.None of these
11 A certain number when divided by 899 leaves a remainder of 63. What will be the remainder when the same number is divided by 24 ?
A.5 B.2 C.4 D.3
12 When 75% of a two digit number is added to it, the digits of the number are reversed. Find the ratio of the unit's digit to the ten's digit in the original number?
A.1:2 B.1:3 C.1:4 D.2:1
13 The HCF and LCM of two numbers are 13 and 455 respectively . If one of the numbers lies between 75 and 125, then that number is
A.91 B.78 C.117 D.104
14 If three consecutive positive even numbers are such that thrice the second number exceeds the sum of first and third number by ten, then third number is
A.12 B.14 C.10 D.16
15 The least number which being increased by 1 will be exactly divisible by 18, 22, 33,and 108 is
A.593 B.1187 C.296 D.2375
16 N= 2x 4x 6x 8 x10 ..........100. How many zeros are there at the end of N?
A.24 B.13 C.12 D.15
17 What is the remainder when by 1723 is divided by 16?
A.0 B.1 C.2 D.3 E.15
18 If V = 10! + 11! + 12! + 13! + 14! + ........+ 999! + 1000!, then what is the unit digit of V?
A.0 B.3 C.1 D.8
19 How many zeros are there at the end of the product 33 x 175 x 180 x 12 x 44 x 80 x 66?
A.2 B.4 C. 5 D. 6
20 What is the greatest power of 5 that divides 30! exactly?
A.5 B.6 C.7 D.8
21 If the sum of two natural numbers is multiplied by each number separately ,the product so obtained are 2418 and 3666. What is the difference between the numbers?
A. 16 B. 26 C.22 D.35
22 461 + 462+ 463+ 464+ 465 is divisible by
A. 3 B.11 C.5 D.17
23 4a56 is a four digit number divisible by 33. What is the value of a?
A. 3 B.4 C.5 D.6
24 N= 5656 +56 .What would be the remainder when N is divided by 57?
A. 0 B. 56 C.55 D.1
25 The sum of two natural numbers is 85 and their LCM is 102. Find the numbers?
A.51&34 B.50&35 C.60&25 D.45&40 E.17&68
26 Let N be the greatest number that will divide 1305, 4665 and 6905, leaving the same remainder in each case. Then sum of the digits in N is:
A.4 B.5 C.6 D.8
27 The least multiple of 7, which leaves a remainder of 4, when divided by 6, 9, 15 and 18 is:
A.74 B.94 C.184 D.364
28 It is being given that (232 + 1) is completely divisible by a natural number. Which of the following numbers is completely divisible by this number?
A.(216 +1) B.(216_1) C.(7x223) D.(296+1)
29 On dividing a number by 5, we get 3 as remainder. What will the remainder when the square of the this number is divided by 5 ?
A.0 B.1 C.2 D.4
30 A 3-digit number 4a3 is added to another 3-digit number 984 to give a 4-digit number 13b7, which is divisible by 11. Then, (a + b) = ?
A.10 B.11 C.12 D.15
31 If n is a natural number, then (6n2 + 6n) is always divisible by:
A.6 only B.6 and 12 both C.18 only D.12 only
32 A two-digit number is such that cube of its 24th part is the same as the number obtained by interchanging the digit of the number. What is the number?
A.24 B.48 C.72 D.96 E.None of these
33 Six bells commence tolling together and toll at intervals of 2, 4, 6, 8 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together ?
A.4 B.10 C.15 D.16
34 If N=1/2+1/6+1/12+1/20+1/30+..............1/156, then the value of N is
A. 12/13 B.1/13 C.13/12 D.None of these
35 A heap of coconuts is divided into groups of 2, 3 and 5 and each time one coconut is left out. The least number of coconuts in the heap is
A.31 B.41 C.51 D.61
36 How many three-digit numbers are divisible by 6 in all
A.100 B.150 C.166 D.196
37 The least number when divided by 35 leaves a remainder 25, when divided by 45 leaves a remainder 35, and when divided by 55 leaves the remainder 45. The number is
A.2515 B.3455 C.2875 D.None of these
38 The sum of the two positive numbers is twice their difference . If their product is 48, the numbers could be
A.3 and 16 B.6 and 8 C.4 and 12 D.None of these
39 When a polynomial of degree 7 is added to a polynomial of degree 5 , the degree of the resulting polynomial is
A.12 B.2 C.5 D.7
40 The ratio between a two-digit number and the sum of the digits of that number is 4:1 . If the digit in the unit's place is 3 more than the digit in the ten's place , what is the number
A.69 B.25 C.36 D.None of these
41 If the product of three consecutive integers is 720, then their sum is
A.27 B.45 C.18 D.54
42 The difference between two numbers is 1365. When the larger one is divided by the smaller one, the quotient is 6 and the remainder is 15. The smaller number is
A.240 B.360 C.270 D.295
43 243 has been divided into three parts such that half of the first part , one - third of the second part and one-fourth of the third part are equal. The largest part is
A.74 B.86 C.92 D.108
44 Which of the following is exactly divisible by 99
A.114345 B.135792 C.3572404 D.913464
45 The numbers which is formed by writing any digit six times (111111, 444444) is always divisible by
A.7 B.11 C.13 D.All of these
46 The number nearest to 99547 which is exactly divisible by 687 is
A.100166 B.98928 C.99579 D.99615
47 Which largest number of five digits is divisible by 99
A.99999 B.99981 C.99909 D.99990
48 Which smallest number of six digits is divisible by 111
A.111111 B.110011 C.100011 D.None of these
49 If n is any positive integer , then (34n- 43n) is always divisible by
A.7 B.17 C.112 D.145
50 The expression 1/(1.2 )+ 1/2.3+ 1/3.4+.............+1/(n(n+1)) for any natural number n is
A.always greater than 1 B.always less than 1 C.always equal to 1 D.not definite
51 In a division sum, the remainder is 0. As student mistook the divisor by 12 instead of 21 and obtained 35 as quotient. What is the correct quotient
A.0 B.12 C.13 D.20
52 On multiplying a number by 7, the product is a number each of whose digits is 3. The smallest such number is
A.47619 B.47719 C.48619 D.47649
53 What will be the remainder when 17200 is divided by 18
A.17 B.16 C.1 D.2
54 A number when divided successively by 4 and 5 leaves remainders 1 and 4 respectively. When it is successively divided by 5 and 4 then the respective remainders will be
A.1,2 B.2,3 C.3,2 D.4,1
55 Which one of the following is the common factor of (4743+4343) and (4747+ 4347)
A.(47-43) B.(47+43) C.(4743+ 4343) D.None of these
56 (1 - 1/n ) + ( 1 - 2/n ) + ( 1 - 3/n ) + .......upto n terms = ?
A.n/2 B.((n-1))/2 C.(n(n-1))/2 D.None of these
57 On dividing 2272 as well as 875 by 3-digit number N, we get the same remainder. The sum of the digits of N is:
A. 10 B. 11 C. 12 D. 13
58 The sum of the two numbers is 12 and their product is 35. What is the sum of the reciprocals of these numbers ?
A.12/35 B.1/35 C.35/8 D.7/32
59 The product of two numbers is 2028 and their H.C.F. is 13. The number of such pairs is:
A. 1 B. 2 C. 3 D. 4
60 The least number which should be added to 2497 so that the sum is exactly divisible by 5, 6, 4 and 3 is:
A. 3 B. 13 C. 23 D. 33
61 The least number which when divided by 5, 6 , 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is:
A. 1677 B. 1683 C. 2523 D. 3363
62 What will be the least number which when doubled will be exactly divisible by 12, 18, 21 and 30 ?
A. 196 B. 630 C. 1260 D. 2520
63 The greatest possible length which can be used to measure exactly the lengths 7 m, 3 m 85 cm, 12 m 95 cm is:
A. 15 cm B. 25 cm C. 35 cm D. 42 cm
64 The sum of two numbers is 528 and their HCF is 33. The numbers of pairs of numbers satisfying the above conditions is
A.4 B.6 C.8 D.12
65 The number of number-pairs lying between 40 and 100 with their HCF as 15 is
A.3 B.4 C.5 D.6
66 The HCF of two numbers is 12 and their difference is 12. The numbers are
A.66,78 B.70,82 C.84,96 D.94, 106
67 The product of two numbers is 4107. If the HCF of these numbers is 37, then the greater number is
A.101 B.107 C.111 D.185
68 The LCM of two numbers is 48. The numbers are in the ratio 2 :3 . The sum of the numbers is
A.28 B.32 C.40 D.64
69 Three numbers are in the ratio of 3: 4: 5 and their LCM is 2400. Their HCF is
A.40 B.80 C.120 D.200
70 The sum of two numbers is 2000 and their LCM is 21879. The two numbers is
A.1993, 7 B.1991,9 C.1989, 11 D.1987,13
71 The HCF and LCM of two numbers are 84 and 21 respectively. If the ratio of two numbers is 1:4 , then the larger of the two numbers is
A.12 B.48 C.84 D.108
72 The LCM of two numbers is 495 and their HCF is 5. If the sum of the numbers is 10, then their difference is
A.10 B.46 C.70 D.90
73 The product of the LCM and HCF of two numbers is 24. The difference of two numbers is 2. Find the numbers
A.2and4 B.6and4 C.8 and 6 D.8 and 10
74 The LCM of two numbers is 45 times their HCF . If one number is 125 and the sum of HCF and LCM is 1150 , the other number is
A.215 B.220 C.225 D.235
75 The HCF and LCM of two numbers are 50 and 250 respectively. If the first number is divided by 2, the quotient is 50 . The second number is
A.50 B.100 C.125 D.250
76 Product of two co-prime numbers is 117. Their LCM should be
A.1 B.117 C.equal to their HCF D.cannot be calculated
77 The LCM of three different numbers is 120. Which of the following cannot be their HCF
A.8 B.12 C.24 D.35
78 The HCF of two numbers is 8. Which one of the following cannot be their LCM
A.24 B.48 C.56 D.60
79 The HCF of two numbers is 23 and other two factors of their LCM are 13 and 14 . The larger of two numbers is
A.276 B.299 C.322 D.345
80 About the number of pairs which have 16 as their HCF and 136 as their LCM , we can definitely say that
A.no such pair exists B.only one such pair exists C.only two such pairs exist D.many such pairs exist
81 7 is added to a certain number ; the sum is multiplied by 5; the product is divided by 9 and 3 is subtracted from the quotient. The remainder left is 12. The number is
A.20 B.30 C.40 D.60
82 By how much is three-fifth of 350 greater than four-seventh of 210
A.95 B.110 C.120 D.210 E.None of these
83 The smallest fraction which should be subtracted from the sum of 1.3/4, 2.1/2, 5.7/12 , 3.1/3 , 2.1/4 to make the result a whole number is
A.5/12 B.7/12 C.1/2 D.7
84 A student was asked to solve the fraction ( 7/3 + 1.1/2 of 5/3 )/( 2 + 1.2/3) and his answer was 1/4 . By how much was his answer wrong
A.1 B.1/55 C.1/220 D.None of these
85 Product of two positive integers is 15210 and their HCF is 39. How many such pairs are possible?
A.1 B.2 C.3 D.4 E.None of these
86 There are four prime numbers written in ascending order of magnitude. The product of first three is 385 and that of last three is 1001. Find the first number?
A.5 B.7 C.11 D.17 E.19
87 2! + 4 ! + 6! + 8 ! + 10! +...........100! when divided by 3, would leave remainder
A.0 B.1 C.2 D.3
88 If x is a prime such that (x2+3) is also a prime, then x can have
A.two values B.one value C.more than two values D.None of these
89 If f(x) = sum of the digits of x , where x is a natural number, then what is the value of f(101)+f(102)+f(103)+...........f(200)?
A.1000 B.784 C.999 D.1001
90 What is the highest power of 31 in 1000! ?
A.31 B.32 C.33 D.None of these
91 What is the last digit of the number 23457194321 ?
A.9 B.1 C.3 D.7
92 A boy was asked to multiply a number by 25. He instead multiplied the number by 52 and got the answer 324 more than the correct answer . The number to be multiplied was
A.12 B.15 C.25 D.32
93 A boy multiplied 423 by a number and obtained 65589 as his answer. If both the fives in the answer are wrong and all other figures are correct , the correct answer is
A.60489 B.61189 C.62189 D.62389
94 When a ball bounces , it rises to 3/4 of the height from which it fell. If the ball is dropped from a height of 32 m, how high will it rise at the third bounce
A.13m B.13.1/2 m C.14.1/2 m D.None of these
95 The sum of three fractions is 2.11/24 . When the largest fraction is divided by the smallest , the fraction thus obtained is 7/6 which is 1/3 more than the middle one. The fractions are
A.3/5 , 4/7 , 2/3 B.7/8 , 5/6 , 3/4 C.7/9 , 2/3 , 3/5 D.None of these
96 A student was asked to find the value of 3/8 of a sum of money. The student made a mistake by dividing the sum by 3/8 and thus got an answer which exceeded the correct answer by Rs 55. The correct answer was
A.Rs 9 B.Rs 18 C.Rs 24 D.Rs 64
97 If we multiply a fraction by itself and divide the product by its reciprocal, the fraction thus obtained is 18 26/27 . The original fraction is
A.8/27 B.1 1/3 C. 2 2/3 D.None of these
98 What is the unit digit in ( 795 - 358 )
A.0 B.4 C.6 D.7
99 What is the unit digit in the 63741793 x 625317 x341491
A.0 B.2 C.3 D.5
100 What is the remainder when 192319241925 is divided by 1924
A.1922 B.1923 C.1 D.None of these