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InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 51. |
The sum of how many terms of the series 6 + 12 + 18 + 24 + ... is 1800 ? |
| Answer» This is an A.P. in which a = 6, d = 6 and Sn = 1800 Then, n [2a + (n - 1)d] = 1800 2 n [2 x 6 + (n - 1) x 6] = 1800 2 3n (n + 1) = 1800 n(n + 1) = 600 n2 + n - 600 = 0 n2 + 25n - 24n - 600 = 0 n(n + 25) - 24(n + 25) = 0 (n + 25)(n - 24) = 0 n = 24 Number of terms = 24. | |
| 52. |
(51+ 52 + 53 + ... + 100) = ? |
| Answer» This is an A.P. in which a = 51, l = 100 and n = 50. Sum = n (a + l) = 50 x (51 + 100) = (25 x 151) = 3775. 2 2 | |
| 53. |
1904 x 1904 = ? |
| Answer» 1904 x 1904 = (1904)2 = (1900 + 4)2 = (1900)2 + (4)2 + (2 x 1900 x 4) = 3610000 + 16 + 15200. = 3625216. | |
| 54. |
What is the unit digit in(7 - 3)? |
| Answer» Unit digit in 795 = Unit digit in [(74)23 x 73] = Unit digit in [(Unit digit in(2401))23 x (343)] = Unit digit in (123 x 343) = Unit digit in (343) = 3 Unit digit in 358 = Unit digit in [(34)14 x 32] = Unit digit in [Unit digit in (81)14 x 32] = Unit digit in [(1)14 x 32] = Unit digit in (1 x 9) = Unit digit in (9) = 9 Unit digit in (795 - 358) = Unit digit in (343 - 9) = Unit digit in (334) = 4. So, Option B is the answer. | |
| 55. |
5358 x 51 = ? |
| Answer» 5358 x 51 = 5358 x (50 + 1) = 5358 x 50 + 5358 x 1 = 267900 + 5358 = 273258. | |
| 56. |
The sum of first five prime numbers is: |
| Answer» Required sum = (2 + 3 + 5 + 7 + 11) = 28. Note: 1 is not a prime number. Definition: A prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself. | |
| 57. |
The smallest 6 digit number exactly divisible by 111 is: |
| Answer» The smallest 6-digit number 100000. 111) 100000 (900 999 ----- 100 --- Required number = 100000 + (111 - 100) = 100011. | |
| 58. |
The largest 5 digit number exactly divisible by 91 is: |
| Answer» Largest 5-digit number = 99999 91) 99999 (1098 91 --- 899 819 ---- 809 728 --- 81 --- Required number = (99999 - 81) = 99918. | |
| 59. |
The smallest 5 digit number exactly divisible by 41 is: |
| Answer» The smallest 5-digit number = 10000. 41) 10000 (243 82 --- 180 164 ---- 160 123 --- 37 --- Required number = 10000 + (41 - 37) = 10004. | |
| 60. |
The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ? |
| Answer» Let the smaller number be x. Then larger number = (x + 1365). x + 1365 = 6x + 15 5x = 1350 x = 270 Smaller number = 270. | |
| 61. |
How many terms are there in the G.P. 3, 6, 12, 24, ... , 384 ? |
| Answer» Here a = 3 and r = 6 = 2. Let the number of terms be n. 3 Then, tn = 384 arn-1 = 384 3 x 2n - 1 = 384 2n-1 = 128 = 27 n - 1 = 7 n = 8 Number of terms = 8. | |
| 62. |
9548 + 7314 = 8362 + (?) |
| Answer» 9548 16862 = 8362 + x + 7314 x = 16862 - 8362 ----- = 8500 16862 ----- | |
| 63. |
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 ? |
| Answer» Number = (12 x 35) Correct Quotient = 420 ÷ 21 = 20 | |
| 64. |
2 + 2 + 2 + ... + 2 = ? |
| Answer» This is a G.P. in which a = 2, r = 22 = 2 and n = 9. 2 Sn = a(rn - 1) = 2 x (29 - 1) = 2 x (512 - 1) = 2 x 511 = 1022. (r - 1) (2 - 1) | |
| 65. |
If the number 517*324 is completely divisible by 3, then the smallest whole number in the place of * will be: |
| Answer» Sum of digits = (5 + 1 + 7 + x + 3 + 2 + 4) = (22 + x), which must be divisible by 3. x = 2. | |
| 66. |
The smallest 3 digit prime number is: |
| Answer» The smallest 3-digit number is 100, which is divisible by 2. 100 is not a prime number. 101 < 11 and 101 is not divisible by any of the prime numbers 2, 3, 5, 7, 11. 101 is a prime number. Hence 101 is the smallest 3-digit prime number. | |
| 67. |
The sum of even numbers between 1 and 31 is: |
| Answer» Let Sn = (2 + 4 + 6 + ... + 30). This is an A.P. in which a = 2, d = 2 and l = 30 Let the number of terms be n. Then, a + (n - 1)d = 30 2 + (n - 1) x 2 = 30 n = 15. Sn = n (a + l) = 15 x (2 + 30) = (15 x 16) = 240. 2 2 | |
| 68. |
If the number 91876 * 2 is completely divisible by 8, then the smallest whole number in place of * will be: |
| Answer» Then number 6x2 must be divisible by 8. x = 3, as 632 is divisible 8. | |
| 69. |
2056 x 987 = ? |
| Answer» 2056 x 987 = 2056 x (1000 - 13) = 2056 x 1000 - 2056 x 13 = 2056000 - 26728 = 2029272. | |
| 70. |
On multiplying a number by 7, the product is a number each of whose digits is 3. The smallest such number is: |
| Answer» By hit and trial, we find that 47619 x 7 = 333333. | |
| 71. |
(?) + 3699 + 1985 - 2047 = 31111 |
| Answer» x + 3699 + 1985 - 2047 = 31111 x + 3699 + 1985 = 31111 + 2047 x + 5684 = 33158 x = 33158 - 5684 = 27474. | |
| 72. |
If the number 481 * 673 is completely divisible by 9, then the smallest whole number in place of * will be: |
| Answer» Sum of digits = (4 + 8 + 1 + x + 6 + 7 + 3) = (29 + x), which must be divisible by 9. x = 7. | |
| 73. |
The difference between the local value and the face value of 7 in the numeral 32675149 is |
| Answer» (Local value of 7) - (Face value of 7) = (70000 - 7) = 69993 | |
| 74. |
(?) - 19657 - 33994 = 9999 |
| Answer» 19657 Let x - 53651 = 9999 33994 Then, x = 9999 + 53651 = 63650 ----- 53651 ----- | |
| 75. |
If the number 653 is divisible by 90, then ( + ) = ? |
| Answer» 90 = 10 x 9 Clearly, 653xy is divisible by 10, so y = 0 Now, 653x0 is divisible by 9. So, (6 + 5 + 3 + x + 0) = (14 + x) is divisible by 9. So, x = 4. Hence, (x + y) = (4 + 0) = 4. | |
| 76. |
3897 x 999 = ? |
| Answer» 3897 x 999 = 3897 x (1000 - 1) = 3897 x 1000 - 3897 x 1 = 3897000 - 3897 = 3893103. | |
| 77. |
What is the unit digit in 7 ? |
| Answer» Unit digit in 7105 = Unit digit in [ (74)26 x 7 ] But, unit digit in (74)26 = 1 Unit digit in 7105 = (1 x 7) = 7 | |
| 78. |
106 x 106 - 94 x 94 = ? |
| Answer» 106 x 106 - 94 x 94 = (106)2 - (94)2 = (106 + 94)(106 - 94) [Ref: (a2 - b2) = (a + b)(a - b)] = (200 x 12) = 2400. | |
| 79. |
If (64) - (36) = 20 x , then = ? |
| Answer» 20 x x = (64 + 36)(64 - 36) = 100 x 28 x = 100 x 28 = 140 20 | |
| 80. |
If and are the two digits of the number 653 such that this number is divisible by 80, then + = ? |
| Answer» 80 = 2 x 5 x 8 Since 653xy is divisible by 2 and 5 both, so y = 0. Now, 653x is divisible by 8, so 13x should be divisible by 8. This happens when x = 6. x + y = (6 + 0) = 6. | |
| 81. |
What is the unit digit in (4137)? |
| Answer» Unit digit in (4137)754 = Unit digit in {[(4137)4]188 x (4137)2} =Unit digit in { 292915317923361 x 17114769 } = (1 x 9) = 9 | |
| 82. |
587 x 999 = ? |
| Answer» 587 x 999 = 587 x (1000 - 1) = 587 x 1000 - 587 x 1 = 587000 - 587 = 586413. | |
| 83. |
A number was divided successively in order by 4, 5 and 6. The remainders were respectively 2, 3 and 4. The number is: |
| Answer» 4 | x z = 6 x 1 + 4 = 10 ----------- 5 | y -2 y = 5 x z + 3 = 5 x 10 + 3 = 53 ----------- 6 | z - 3 x = 4 x y + 2 = 4 x 53 + 2 = 214 ----------- | 1 - 4 Hence, required number = 214. | |
| 84. |
(2 + 4 + 6 + ... + 20) = ? |
| Answer» (22 + 42 + 62 + ... + 202) = (1 x 2)2 + (2 x 2)2 + (2 x 3)2 + ... + (2 x 10)2 = (22 x 12) + (22 x 22) + (22 x 32) + ... + (22 x 102) = 22 x [12 + 22 + 32 + ... + 102] Ref: (12 + 22 + 32 + ... + n2) = 1 n(n + 1)(2n + 1) 6 = 4 x 1 x 10 x 11 x 21 6 = (4 x 5 x 77) = 1540. | |
| 85. |
35 + 15 x 1.5 = ? |
| Answer» Given Exp. = 35 + 15 x 3 = 35 + 45 = 35 + 22.5 = 57.5 2 2 | |
| 86. |
The sum of first 45 natural numbers is: |
| Answer» Let Sn = (1 + 2 + 3 + ... + 45) This is an A.P. in which a = 1, d = 1, n = 45 and l = 45 Sn = n (a + l) = 45 x (1 + 45) = (45 x 23) = 1035 2 2 Required sum = 1035. | |
| 87. |
666 ÷ 6 ÷ 3 = ? |
| Answer» Given Exp. = 666 x 1 x 1 = 37. 6 3 | |
| 88. |
The sum of all two digit numbers divisible by 5 is: |
| Answer» Required numbers are 10, 15, 20, 25, ..., 95 This is an A.P. in which a = 10, d = 5 and l = 95. tn = 95 a + (n - 1)d = 95 10 + (n - 1) x 5 = 95 (n - 1) x 5 = 85 (n - 1) = 17 n = 18 Requuired Sum = n (a + l) = 18 x (10 + 95) = (9 x 105) = 945. 2 2 | |
| 89. |
The difference between the place values of two sevens in the numeral 69758472 is |
| Answer» Required difference = (700000 - 70) = 699930 | |
| 90. |
On dividing a number by 68, we get 269 as quotient and 0 as remainder. On dividing the same number by 67, what will the remainder ? |
| Answer» Number = 269 x 68 + 0 = 18292 67) 18292 (273 134 ---- 489 469 ---- 202 201 --- 1 --- Therefore, Required remainder = 1 | |
| 91. |
What is the unit digit in the product (3 x 6 x 7)? |
| Answer» Unit digit in 34 = 1 Unit digit in (34)16 = 1 Unit digit in 365 = Unit digit in [ (34)16 x 3 ] = (1 x 3) = 3 Unit digit in 659 = 6 Unit digit in 74 Unit digit in (74)17 is 1. Unit digit in 771 = Unit digit in [(74)17 x 73] = (1 x 3) = 3 Required digit = Unit digit in (3 x 6 x 3) = 4. | |
| 92. |
3251 + 587 + 369 - ? = 3007 |
| Answer» 3251 Let 4207 - x = 3007 + 587 Then, x = 4207 - 3007 = 1200 + 369 ---- 4207 ---- | |
| 93. |
7589 - ? = 3434 |
| Answer» Let 7589 -x = 3434 Then, x = 7589 - 3434 = 4155 | |
| 94. |
217 x 217 + 183 x 183 = ? |
| Answer» (217)2 + (183)2 = (200 + 17)2 + (200 - 17)2 = 2 x [(200)2 + (17)2] [Ref: (a + b)2 + (a - b)2 = 2(a2 + b2)] = 2[40000 + 289] = 2 x 40289 = 80578. | |
| 95. |
The unit digit in the product (784 x 618 x 917 x 463) is: |
| Answer» Unit digit in the given product = Unit digit in (4 x 8 x 7 x 3) = (672) = 2 | |
| 96. |
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 |
| Answer» 4 | x y = (5 x 1 + 4) = 9 -------- 5 | y -1 x = (4 x y + 1) = (4 x 9 + 1) = 37 -------- | 1 -4 Now, 37 when divided successively by 5 and 4, we get 5 | 37 --------- 4 | 7 - 2 --------- | 1 - 3 Respective remainders are 2 and 3. | |
| 97. |
8796 x 223 + 8796 x 77 = ? |
| Answer» 8796 x 223 + 8796 x 77 = 8796 x (223 + 77) [Ref: By Distributive Law ] = (8796 x 300) = 2638800 | |
| 98. |
8988 ÷ 8 ÷ 4 = ? |
| Answer» Given Exp. = 8988 x 1 x 1 = 2247 = 280.875 8 4 8 | |
| 99. |
287 x 287 + 269 x 269 - 2 x 287 x 269 = ? |
| Answer» Given Exp. = a2 + b2 - 2ab, where a = 287 and b = 269 = (a - b)2 = (287 - 269)2 = (182) = 324 | |
| 100. |
3 + 33 + 333 + 3.33 = ? |
| Answer» 3 + 33 + 333 + 3.33 ------ 372.33 ------ | |