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81. N is the smallest three digit prime number. When N is divided by 13, then what will be the reminder?
- A. 8
- B. 9
- C. 7
- D. 10
Answer: 10
Explanation: The smallest three digit prime number (N)=101 Remainder after dividing 101by 13 = 10
82. How many natural numbers are there between 1000 to 2000, which when divided by 341 leaves remainder 5 ?
- A. 3
- B. 2
- C. 4
- D. 1
Answer: 3
Explanation: Natural numbers between 1000 and 2000 = 1000 < 341 K + 5 < 2000 Where K is taken as 3, 4, 5 K = 3 then 341 K + 5 = 341×3+5 = 1028 K = 4 then 341 K + 5 = 341 × 4 + 5 = 1369 K = 5 then 341 K + 5 = 341 × 5 + 5 = 1710 Hence the numbers of natural numbers between 1000 and 2000 are three (1028, 1369, 1710) which when divided by 341 leaves 5 as a remainder Trick: 2000 341 = Integer quotient = 5 And 1000341 = Integer quotient = 2 ∴ The natural numbers b/w 1000 to 2000 which when divided by 341 leaves 5 as a remainder = 5 - 2 = 3
83. M is the largest three digit number which when divided by 6 and 5 leaves remainder 5 and 3 respectively. What will be the remainder when M is divided by 11 ?
- A. 1
- B. 2
- C. 3
- D. 4
Answer: 4
Explanation: The largest 3-digit number which when divided by 6 and 5 leaves remainder as 5 and 3 998, 993, 988, 983 Hence 983 is that number which when divided by 6 and 5 leaves remainder 5 and 3 Respectively ⇒M = 983 ⇒M ÷ 11 = 983 ÷ 11 remainder = 4
84. If 5 divided the integer n, the remainder is 2 . What will be the remainder if 7n is divided by 5?
- A. 1
- B. 3
- C. 2
- D. 4
Answer: 4
Explanation: Let integer (n) = 7 Remainder obtained after dividing 7 by 5 = 2 7n = 49 Remainder Obtained after dividing 7n by 5 = 4
85. If 7 divided a positive integer n, the remaind er is 2. Which of the following numbers gives a reminder of 0 when divided by 7?
- A. n + 5
- B. n - 5
- C. n + 2
- D. n + 1
Answer: n + 5
Explanation: Let n = 9 Remainder obtained after dividing n by 7 = 2 From option, n + 5 = 14 is exactly divisible by 7
86. A divisor is 15 times the quotient and 3 times the remainder. If the remainder is 40, find the dividend.
- A. 900
- B. 600
- C. 750
- D. 1000
Answer: 1000
87. When an integer n is divided by 7, so the remainder is 3. If 6n is divided by 7, what will be the remainder?
- A. 1
- B. 4
- C. 0
- D. 2
Answer: 4
88. The ratio of divisor and remainder is 3 : 2 an d ratio of divisor and quotient is 7:12. If remainder is 14 then what is the remainder obtained when the dividend is divided by 9?
- A. 3
- B. 6
- C. 4
- D. 5
Answer: 5
Explanation: The ratio of divisor and remainder = 3 : 2 Let the divisor and remainder be 3x and 2x respectively. And ratio of divisor and quotient = 7 : 12 = 7y, 12y if remainder = 14 then 2x = 14 ⇒ x = 7 Then, divisor 3x = 3×7 = 21, but divisor is 7y then 7y = 21, y = 3 then quotient 12y = 12×3 = 36 Now, dividend = divisor × quotient + remainder dividend = 21×36+14 = 770 Then the remainder obtained on dividing the dividen d by 9 = remainder = 5
89. When an integer n is divided by 6, the remainder is 5. What is the remainder if 9n is divided by 6?
- A. 4
- B. 3
- C. 5
- D. 2
Answer: 4
Explanation: (b) When an integer n is divided by 6, the remainder is 5. ∴∴ ∴∴ Number = Divisor × Quotient + Remainder ⇒ n = 6q +5 According to the question, If 9n is divided by 6, ∴9n = 9 (6q + 5) ⇒ 9n = 54q + 45 ⇒ 9n = 54q + 42 +3 ⇒ 9n = 6(9q + 7) + 3 So, 3 is remainder if 9n is divided by 6. Hence, option (b) is correct.
90. If a number is divisible by 624, the remainder will be 53. If the same number is divisible by 16, then the remainder will be
- A. 5
- B. 4
- C. 7
- D. 6
Answer: 5
91. Let x be the least number which when divided by 8, 9, 12, 14 and 36 leaves a remainder of 4 in each case, but x is divisible by 11. The sum of the digits of x is____.
- A. 5
- B. 9
- C. 4
- D. 6
Answer: 4
Explanation: LCM of 8, 9, 12, 14 and 36 = 504 Let the smallest number be x = 504 × m + 4 According to question number, (504 × m + 4), is divisible by 11 Hence on putting, m = 2 x = 1012 Sum of digits of 1012 = 1+0+1+2 = 4
92. When a number M is divided by 7, the remainder is 6. What is the remainder if the square of M is divided by 7?
- A. 3
- B. 4
- C. 1
- D. 2
Answer: 1
Explanation: If M is divided by 7, the remainder is 6 that can be written as, M = 7x + 6 for integer x. Then, M2 is divided by 7 that can be written as, M2 = (7x + 6)2 = 49x2 + 84x + 36 = 49x2 + 84x + 35 +1 So, (49x 2 + 84x + 35) is divisible by 7 and leaves remainder 1. Hence, option (c) is correct.
93. When 3738, 5659 and 9501 are divided by the greatest possible number x, the remainder in each case is y. What is the sum of x and y?
- A. 3738
- B. 3673
- C. 3637
- D. 3783
Answer: 3738
Explanation: The remainder left in each case is y HCF of 1921 , 3842 and 5763x = 1921 The remainder obtained after dividing each by 1921 (y) = 1817 ∴ x = 1921, y = 1817 Hence x + y = 3738
94. If a number is divided by 3, the remainder wil l be 2. If the number is added by 5 and then divided by 3, then what will be the reminder?
- A. 0
- B. 3
- C. 1
- D. 2
Answer: 1
95. When a number is divided by 14, the remainder is 9. If the square of the same number is divided by 14, then the remainder will be
- A. 11
- B. 9
- C. 8
- D. 10
Answer: 11
Explanation: Let the number be 23. On dividing 23 by 14 the remainder is 9. Again, on dividing (23)2 = 529 by 14 the remainder is 11.
96. If a positive integer n is divided by 7, the remainder is 2. Which of the numbers in the options yields a remainder of 0 when it is divided by 7?
- A. n + 5
- B. n + 2
- C. n + 3
- D. n + 1
Answer: n + 5
97. When a number is divided by 3, the remainder is 2. Again, when the quotient is divided by 7, the remainder is 5. What will be the remainder when the original number is divided by 21?
- A. 14
- B. 13
- C. 17
- D. 16
Answer: 17
Explanation: Let, the original number be N According to the question- N = 3q + 2 Again, q = 7×1 + 5 q = 12 Then, N = 3×12+2 N = 38 Now, when 38 are divided by 21, we get 17 as remainder.
98. Given n an integer what is the remainder when (6n +3)2 is divided by 9?
- A. 2
- B. 3
- C. 1
- D. 0
Answer: 0
99. The product of two numbers is 225. If one of the number is 45, then what is the another number?
- A. 3
- B. 15
- C. 5
- D. 7
Answer: 3
100. If the integer 'n' is divided by 5, the remain der is 2. What will be the remainder when 7n is divided by 5?
- A. 1
- B. 3
- C. 2
- D. 4
Answer: 4
101. When two numbers are separately divided by 44 the remainders are 11 and 38 respectively. If the sum of the two number is divided by 44, then the obtained remainder will be
- A. 16
- B. 33
- C. 5
- D. 44
Answer: 5
Explanation: Let the numbers be x and y. According to question:- x = p × 44 + 11 y = q × 44 + 38 So, adding these numbers we get, x + y = (p × 44 + 11) + (q × 44 + 38) x + y = (p + q) × 44 + 44 + 5 x + y = 44 (p + q + 1) + 5 Hence, the remainder obtained when of the number by 44 will be 5.
102. What is the greatest number by which 156, 181 and 331 are divided the remainder is 6 in each case?
- A. 17
- B. 25
- C. 13
- D. 26
Answer: 25
Explanation: QThe remainder is '6' in each case. 156 - 6 = 150 181 - 6 = 175 331 - 6 = 325 HCF of 150, 175, and 325 HCF= 25 So, the required greatest number = ‘25’
103. What will be remainder when 8127 is divided by 8?
- A. 4
- B. 7
- C. 6
- D. 5
Answer: 7
Explanation: According to the question, So, the remainder is 7.
104. Find the smallest possible number which when divided by 16, 24, and 28 leaves remainder 13, 21 and 25 respectively?
- A. 320
- B. 348
- C. 336
- D. 333
Answer: 333
Explanation: From the question :- 16 - 13 = 3 24 - 21 = 3 28 - 25 = 3 The difference is same So, L.C.M of 16, 24 and 28 = 336 Hence, the required number = 336 - 3 = 333
105. Find the smallest number which, when divided by 60,84, and 96 leaves remainder of 28,52 and 64 respectively ?
- A. 3392
- B. 3360
- C. 3318
- D. 3328
Answer: 3328
Explanation: Difference of number and remainder:- ⇒ 60 - 28 = 32 ⇒ 84 - 52 = 32 ⇒ 96 - 64 = 32 Difference is same So, LCM of (60, 84, 96) 60 = 12 × 5 84 = 12 × 7 96 = 12 × 8 L.C.M = 12 × 8 × 7 × 5 = 2×2×2×2×2×3×5×7 = 3360 ∴ Required Smallest number = 3360 - 32 = 3328
106. Find the smallest natural number 'x' that mus t be subtracted from 1800 so that (1800 - x), when divided by 7, 11 and 23, will leave 5 as the remainder in each case.
- A. 24
- B. 25
- C. 20
- D. 26
Answer: 24
Explanation: LCM of 7,11 and 23 = 7 × 11× 23 = 1771 Now So, the smallest natural number (x) = (1800 - 1771) - 5 = 29 - 5 = 24 ⇒ x = 24
107. What is the smallest number which when divided by 18, 24 and 36 leaves 3 as a remainder in each case?
- A. 93
- B. 111
- C. 75
- D. 99
Answer: 75
Explanation: According to question:- Hence, smallest number = (LCM of 18, 24, 36) + 3 = 72 + 3 = 75
108. Find the smallest number which when divided by 19 and 23 gives remainder of 13 and 17 respectively ?
- A. 429
- B. 431
- C. 419
- D. 437
Answer: 431
Explanation: According to the question, 19-13 = 6 23 - 17 = 6 ∴ Smallest Number = (LCM of 19 and 23) - 6 = 437 - 6 = 431
109. Which of the following is the greatest number by which when dividing the numbers 342 and 480, the remainder remains 6 and 4 respectively?
- A. 14
- B. 4
- C. 7
- D. 28
Answer: 28
110. Find the largest number which divides the numbers 394 and 658 and leaves remainder 1 and 3 respectively.
- A. 131
- B. 133
- C. 143
- D. 141
Answer: 131
Explanation: From the question:- 394 - 1 = 393 658 - 3 = 655 Now the required number will be the HCF of 393 and 655 So HCF = 131
111. What is the smallest number which when divided by 6, 8, and 10 leaves remainder 4, 6, and 8 respectively ?
- A. 120
- B. 118
- C. 112
- D. 88
Answer: 118
Explanation: From the question, 6 - 4 = 2, 8 - 6 = 2, 10 - 8 = 2 Since difference is same. ∴ Required smallest number = (LCM of 6, 8 and 10) -2 = 120 - 2 = 118
112. Suppose x be the largest number by which dividing 6564, 7416, and 8907 gives the same remainder in each case. Find the sum of the digits of x.
- A. 6
- B. 9
- C. 10
- D. 5
Answer: 6
Explanation: 7416 - 6564 = 852 8907 - 7416 = 1491 8907 - 6564 = 2343 Hence the largest number (x) = 213 ∴ Sum of the digits of x = 2 +1 +3 = 6
113. When a number is divided by 16, the remainder is 4, when the square of that number is divided by 16, what will be the remainder?
- A. 1
- B. 2
- C. 3
- D. 0
Answer: 0
Explanation: Let the number be x ∵ Dividend = Divisor × Quotient + Remainder According to the question, x = 16 K + 4 On putting k = 1 x = 16 × 1 + 4 = 20 (x)2 = (20)2 = 400 Now, 40016 =0 (Remainder) Hence required remainder will be 0.
114. If a number is divided by 3, the remainder is 2. If 5 is added to this number and divided by 3, what will be the remainder?
- A. 0
- B. 3
- C. 1
- D. 2
Answer: 1
115. When a number is divided by 65, the remainder is 31. When the same number is divided by 13, the remainder is divided.
- A. 7
- B. 5
- C. 3
- D. 9
Answer: 5
Explanation: Let the number be x ∴∴ ∴∴ Number (x) = 1×65+31=96 x= 96 According to question:- Hence, when the number is divided by 13 the remaind er is 5.
116. What is the smallest number which when divided by 15, 25, 35, and 40 leaves remainder 10, 20, 30, and 35 respectively ?
- A. 4210
- B. 4200
- C. 4205
- D. 4195
Answer: 4195
Explanation: From the question, 15-10= 5 25-20 = 5 35-30= 5 40-35= 5 The difference is same Now LCM of 15, 25, 35 and 40 LCM = 2×2×2×3×5×5×7 = 4200 Then required smallest number = 4200-difference = 4200-5 = 4195
117. Find the remainder obtained by dividing (265)4081+9 by 266.
- A. 1
- B. 6
- C. 9
- D. 8
Answer: 8
118. When a number is divided by 7, the remainder is 1. What will be the remainder when the cube of this number is divided by 7?
- A. 2
- B. 4
- C. 1
- D. 3
Answer: 1
Explanation: If dividing a number by 7, the remainder is 1, then dividing the cube of that number by 7, the remainder will be 1. For example :- 38 8 5121(Remainder)and 1(Remainder)7 7 7= = =
119. In a division problem, the divisor is 10 time s the quotient and 5 times the remainder. If the remainder is 46, what will be the dividend?
- A. 4874
- B. 4286
- C. 5972
- D. 5336
Answer: 5336
120. What is largest number which divides the numbers 627,15630 and 3128 and leaves remainder 2, 5 and 3 respectively ?
- A. 775
- B. 625
- C. 1225
- D. 650
Answer: 625
Explanation: Required number = HCF of (627 - 2), (15630 - 5) and (3128 - 3) H.C.F of 625, 15625 and 3125 = 625
121. If x = (164) 169 + (333) 337-(727)726, then what is the unit digit of x ?
- A. 5
- B. 7
- C. 8
- D. 9
Answer: 8
Explanation: x = (164)169 + (333)337 - (727)726 For unit digit divide the power over base by 4 and place the remainder as the power of the unit digit of the base number which is left after dividing by 4 ∴x = (4)1 + (3)1 - (7)2 = 4 + 3 - 49 On writing unit digit x = 4 + 3 - 9 = -2 x = 10 - 2 = 8 Note- 10 is added to unit digit to make it positive .
122. What is the digit at units place in the produc t (653 × 308 × 402 × 413)?
- A. 4
- B. 3
- C. 2
- D. 8
Answer: 4
123. What percentage of the numbers from 101 to 1000 have 9 in the unit's digit?
- A. 10%
- B. 12%
- C. 20%
- D. 15%
Answer: 10%
Explanation: Required number from 101 to 200 = 10 Hence numbers of such number from 101 to 1000 in which unit digit is 9 = 10 × 9 = 90 Total numbers of numbers from 101 to 1000 = 900 Required % 90= ×100 = 10% 900
124. What is the unit digit of (217) 413×(819)547×(414)624×(342)812?
- A. 2
- B. 4
- C. 6
- D. 8
Answer: 8
Explanation: Hence unit digit = 8
125. If the unit digit of 433 × 456 × 43N is (N + 2), then what is the value of N?
- A. 1
- B. 8
- C. 3
- D. 6
Answer: 6
126. If x = (633) 24 - (277)38 + (266)54, what is the unit digit of x?
- A. 8
- B. 6
- C. 4
- D. 7
Answer: 8
127. What is the unit digit of sum of the first 111 whole numbers?
- A. 4
- B. 6
- C. 5
- D. 0
Answer: 5
Explanation: First 111 whole numbers → 0, 1, 2, 3 ........... 110 Sum of first 'n' natural number. (Sn) ⇒ n(n 1)2+ S 110= 110 (110 1)2× + 110 111 55 1112×= = × = 6105 So, unit digit is 5
128. Suppose x = (433) 24 - (377) 38 + (166) 54 then, what is the unit digit of x ?
- A. 6
- B. 9
- C. 8
- D. 7
Answer: 8
Explanation: x = (433)24 - (377)38 + (166)54 → x = 324 - 738 + 654 → x = 3o - 72 + 62 [ ∵ (Base number unit digit) remainder] Hence unit digit of x = (1-9 + 6) x = (7-9) or x = (17-9) ∴ x = 8
129. How many factors of 420 are prime numbers?
- A. 3
- B. 15
- C. 7
- D. 4
Answer: 4
Explanation: 420 = 2×2×3×5×7 Hence prime factors - 2, 3, 5, 7 = 4 Hence there are 4 prime factors of 420
130. How many natural numbers less than 1000 are divisible by 5 or 7 but NOT by 35?
- A. 285
- B. 313
- C. 243
- D. 341
Answer: 285
Explanation: Total natural numbers below 1000 = 999 Total natural numbers which are divisible by 5= 9995 = 199 Total natural numbers which are divisible by 7 = 9997 = 142 Total natural numbers which are divisible by 35 = 999 35 = 28 ∴Total numbers till 999 which are divisible by 5 and 7 but not divisible by 35= (199 + 142 - 2 × 28) = 285
131. How many multiples of 7 are there from 1 to 100 which are not multiples of 4?
- A. 14
- B. 11
- C. 10
- D. 12
Answer: 11
Explanation: Numbers of multiples of 7 from 1 to 100 100 147= = L.C.M of 7 and 4 = 28 Hence from 1 to 100, number divisible by 7 and 4 = 100 328 = number Hence, there are 11 (14 - 3 = 11) numbers which are divisible by 7 but not by 4
132. How many positive factors of 444 are there?
- A. 6
- B. 8
- C. 9
- D. 12
Answer: 6
133. How many positive factors are there in 333?
- A. 5
- B. 8
- C. 6
- D. 9
Answer: 6
134. The number of factors of 3600 is
- A. 42
- B. 44
- C. 45
- D. 43
Answer: 45
Explanation: ∵ We know that If N = 2a × 3b × 5c × 7d........ Then total number of factors = (a+1) (b+1) (c+1) (d+1)..... ∴ 3600 = 24 × 32 × 52 Therefore the number of factors of 3600 = (4+1) (2+1) (2+1) = 5 × 3 × 3 = 45
135. How many two digit prime numbers are there between 10 to 100 which remains prime numbers when the order of their digits is reversed?
- A. 8
- B. 9
- C. 10
- D. 12
Answer: 9
Explanation: Number of prime number between 1 to 100 = 25 Prime number between 1 to 10 = 4 ∴ Prime numbers between 10 to 100 = 21 The required numbers are as follows - , , , 19, 23, 29, , ,41, 43, 47, 53, 59, 61, 67, , , , 83, 89, Hence there are 9 prime numbers which will remain prime numbers after reversing their digits
136. x, y and z are prime numbers and x+y+z = 38. What is maximum value of x?
- A. 19
- B. 23
- C. 31
- D. 79
Answer: 31
Explanation: x + y + z = 38 For the value of x to be maximum the value of y and z must be 2 and 5 respectively x + 2 + 5 = 38 x = 31
137. If A = 1 - 10 + 3 - 12 + 5 - 14 + 7 + ....... upto 60 terms, then what is the value of A ?
- A. -360
- B. -310
- C. -240
- D. -270
Answer: -270
Explanation: Given A = 1-10 + 3 - 12 + 5 - 14 + 7 + ....... up to 60 t erms A = (1-10) + (3-12) + (5-14) + 7 + ......... up to 60 terms ⇒ A = -9 - 9 - 9 - ........ 30 terms ⇒ A = -9 × 30 ⇒ A 270= -
138. x, y, and z are distinct prime numbers, where x < y < z, if x + y + z = 70, then what is the value of z ?
- A. 29
- B. 31
- C. 37
- D. 43
Answer: 37
139. How many of the following number are divisible by 42 ? 2646, 1008, 1470, 656, 2478, 1826
- A. 2
- B. 3
- C. 4
- D. 5
Answer: 4
Explanation: 2646, 1008, 1470, 656, 2478, 1826 Numbers divisible by 42- 2646, 1008, 1470 and 2478 Hence there are 4 numbers which are divisible by 4 2.
140. What least number should be added to 754 so that the number is completely divisible by 59 ?
- A. 21
- B. 13
- C. 16
- D. 7
Answer: 13
Explanation: On adding 59-46 =13 to 754 the number will be exact ly divisible by 59
141. What is the least number added to 700, so that number becomes multiple of 17?
- A. 3
- B. 12
- C. 14
- D. 9
Answer: 3
Explanation: (c) On dividing 700 by 17, we get 3 as a remainder. Hence on adding (17 - 3) 14 to 700 it will becomes multiple of 17.
142. If 2785P3 is divisible by 11, then what will b e the digit in place of P?
- A. 2
- B. 5
- C. 8
- D. 6
Answer: 2
Explanation: (b) Rule of divisibility by 11- When the difference between the sum of digits at odd places and sum of digits at even places of any number is 0 or multiple of 11 then that number will be divisible b y 11 ⇒ (2 + 8 + P) - (7 + 5 + 3) ⇒ (10 + P) - (15) ⇒ P - 5…………(i) ∵ On putting P = 5, the number is divisible by 11. Hence value of P = 5
143. How many numbers between 800 to 2000 are divisible by 13?
- A. 92
- B. 90
- C. 91
- D. 93
Answer: 92
Explanation: Formula, l = a + (n - 1) d where n = Total number of terms d = common difference The numbers divisible by 13 between 800 to 2000 are 806, 819, .............. 1989 From the formula, 1989 = 806 ± (n-1) × 13 1183 = 13(n-1) 91 = (n-1) ∴ n = 91+1= 92 Total numbers divisible by 13 between 800 and 2000 = 92
144. What should be the value of N to make 396258N divisible by 8?
- A. 8
- B. 4
- C. 2
- D. 6
Answer: 4
Explanation: QQ QQ If the last three digits of a number is divisible by 8 then the number will be divisible by 8. ∴ 58N 584 738 8= = Hence, N = 4
145. If 8-digit number 4432A43B is divisible by 9 and 5, then the sum of A and B is equal to
- A. 8
- B. 7
- C. 5
- D. 12
Answer: 7
Explanation: Rule of divisibility for 5 - If the unit digit of any number is 0 or 5 then that number will be divis ible by 5. Rule of divisibility for 9- If the sum of all digits of any number is exactly divisible by 9, then that number will be divisible by 9. The given number is 4432A43B 4432A43B = 4 + 4 + 3 + 2 + A + 4 + 3 + B = 20 + A + B Hence, we can place number 7 in place of A + B So that 20 + (A + B) = 20 + 7 = 27 is divisible by 9 Note - (In place of B there will be only 0 or 5) B = 0 then, A = 7 B = 5 then , A = 2 ⇒ A + B = 7 + 0 = 7 or 2 + 5 = 7
146. If the 8-digit number 43A5325B is divisible by 8 and 9, then the sum of A and B is equal to
- A. 15
- B. 14
- C. 12
- D. 18
Answer: 15
147. If 4M37094267N is divisible by both 8 and 11, where M and N are single digit integers, then the values of M and N are
- A. M = 2, N = 5
- B. M = 5, N = 4
- C. M = 5, N = 2
- D. M = 5, N = 6
Answer: M = 2, N = 5
148. Which of the following numbers will completely divide 781 + 782 + 783?
- A. 389
- B. 387
- C. 397
- D. 399
Answer: 399
Explanation: QDivide the power of the given numbers by 4 and write their remainders as the power of the numbers. 781 + 782 + 783 = 7 1 + 72 + 73 = 7 + 49 + 343 = 350 + 49 = 399
149. Which number is divisible by both 9 and 11?
- A. 10,098
- B. 10,108
- C. 10,087
- D. 10,089
Answer: 10,098
Explanation: Rule of divisibility for 9 : Numbers in which sum of all digits is divisible by 9, that nu mbers are divisible by 9. Rule of divisibility for 11: If the difference between the sum of digits in alternate order is zero or mul tiple of 11 then the number will be exactly divisible by 11. From option (a), 10098 ⇒ 1 + 0 + 0 + 9 + 8 = 18 ∵ 18 is divisible by number 9 and ⇒ 9 - 9 = 0 ∵ Difference is zero Hence, 10098 is exactly divisible by both 9 and 11
150. Which of the following numbers is divisible by 2, 5 and 10?
- A. 149
- B. 7,20,345
- C. 19,400
- D. 1,25,372
Answer: 19,400
Explanation: The number which will be divisible by LCM of 2,5, 10 that will be also divisible by LCM of 2, 5 and 10. LCM of 2, 5 and 10 = 10 Hence those numbers which are divisible by 10 their unit digit will be zero. ∴ From option (c) number '19400' will be divisible b y 2, 5 and 10
151. Which of the following numbers is divisible by both 7 and 11?
- A. 16,324
- B. 16,425
- C. 12,235
- D. 16,257
Answer: 16,324
Explanation: Rule of divisibility for 11 : In any given number the difference between the sum of alternate digits must be 0 or multiple of 11. From option (a), ⇒ 8 - 8 = 0 Divisibility rule of 7 :- The difference between twice the unit digit of the given number and the remaining part of the given number should be a multiple of 7 or it should be equal to '0'. 1632 - 2 4 7 ×= = 232 Hence the number will be divisible by 11. Number 16324 is divisible by given number 7 ∴ Number 16324 is divisible by both 7 and 11.
152. If 2794p561 is divisible by 9, then the value of p is
- A. 2
- B. 4
- C. 0
- D. 3
Answer: 2
Explanation: Rule of divisibility for 9- If the sum of all digits of a number is divisible by 9 then that numb er will be divisible by 9. ∴ Given number = 2794p561 = 2 + 7 + 9 + 4 + p + 5 + 6 + 1 = 34 + p On putting value of p = 2, the number 34 + 2 = 36 w ill be exactly divisible by 9.
153. If the number 59a44b is divisible by 36, then the maximum value of a + b is
- A. 14
- B. 16
- C. 10
- D. 12
Answer: 14
154. Which of the following numbers is divisible by 6?
- A. 23,408
- B. 43,923
- C. 1,00,246
- D. 3,49,722
Answer: 3,49,722
Explanation: The number which is divisible by 6, is also divisible by 2 and 3. Now to be divisible by 2, the last digit of given n umber will be zero or multiple of 2 and to be divisible b y 3, the sum of all digits must be divisible by 3. Hence we will check it from option. In number 3, 49 , 722 last digits are divisible by 2 and sum of digit s = 3+4+9+7+2+2 = 27 which is also divisible by 3. Henc e the number will be divisible by 6.
155. If the 8-digit number 1a765b12 is to be divisible by 72, the least value of (2a + 3b) is
- A. 9
- B. 11
- C. 12
- D. 10
Answer: 11
156. Which are the two nearest numbers to 19596, divisible by 9?
- A. 19,509; 19,611
- B. 19,564; 19,620
- C. 19,611; 19,575
- D. 19,593; 19,602
Answer: 19,593; 19,602
157. What is the least 5-digit number that is divisible by 91?
- A. 10283
- B. 10010
- C. 10101
- D. 10192
Answer: 10010
Explanation: Smallest five digit number = 10000 The smallest number of five digits which is divisib le by 91 = 10000 + (91-81) = 10000 + 10 = 10010
158. If 7129p465 is divisible by 9, then the value of p is
- A. 2
- B. 3
- C. 0
- D. 4
Answer: 2
159. If a positive integer 'n' is divisible by 3, 5 and 7, then what is the next larger integer divisible by all these numbers?
- A. n + 105
- B. n + 35
- C. n + 110
- D. n + 21
Answer: n + 105
Explanation: ∵ Number 'n' is divisible by 3, 5 and 7 ∴ Number 3, 5, 7 are factors of n. Hence the next larger number divisible by these numbers = n + (L.C.M of 3, 5, 7) = n + (3×5×7) = n + 105
160. If 'a' is a natural number, then (7a 2 + 7a) is always divisible by
- A. only 7
- B. Both 7 and 14
- C. only 17
- D. only 21
Answer: Both 7 and 14
Explanation: Qa is a natural number ∴ On taking a = 1, 7a 2 + 7a = 7+7 = 14 On taking a = 2, 7a 2 + 7a = 7×4 + 7×2 = 28 + 14 = 42 On taking a = 3, 7a 2 + 7a = 7×9 + 7×3 = 63+21 = 84 ∴ 14, 42, 84 all numbers are divisible by both 7 and 14 Hence (7a2 + 7a) will always be divisible by both 7 and 14
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