InterviewSolution
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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.
| 1. |
(112 x 5) = ? |
| Answer» (112 x 54) = 112 x 10 4 = 112 x 104 = 1120000 = 70000 2 24 16 | |
| 2. |
The difference between a positive proper fraction and its reciprocal is 9/20. The fraction is: |
| Answer» Let the required fraction be x. Then 1 - x = 9 x 20 1 - x2 = 9 x 20 20 - 20x2 = 9x 20x2 + 9x - 20 = 0 20x2 + 25x - 16x - 20 = 0 5x(4x + 5) - 4(4x + 5) = 0 (4x + 5)(5x - 4) = 0 x = 4 5 | |
| 3. |
If is a natural number, then (6 + 6) is always divisible by: |
| Answer» (6n2 + 6n) = 6n(n + 1), which is always divisible by 6 and 12 both, since n(n + 1) is always even. | |
| 4. |
107 x 107 + 93 x 93 = ? |
| Answer» 107 x 107 + 93 x 93 = (107)2 + (93)2 = (100 + 7)2 + (100 - 7)2 = 2 x [(100)2 + 72] [Ref: (a + b)2 + (a - b)2 = 2(a2 + b2)] = 20098 | |
| 5. |
What will be remainder when (67 + 67) is divided by 68 ? |
| Answer» (xn + 1) will be divisible by (x + 1) only when n is odd. (6767 + 1) will be divisible by (67 + 1) (6767 + 1) + 66, when divided by 68 will give 66 as remainder. | |
| 6. |
What least number must be added to 1056, so that the sum is completely divisible by 23 ? |
| Answer» 23) 1056 (45 92 --- 136 115 --- 21 --- Required number = (23 - 21) = 2. | |
| 7. |
1397 x 1397 = ? |
| Answer» 1397 x 1397 = (1397)2 = (1400 - 3)2 = (1400)2 + (3)2 - (2 x 1400 x 3) = 1960000 + 9 - 8400 = 1960009 - 8400 = 1951609. | |
| 8. |
(1000) ÷ 10 = ? |
| Answer» Given Exp. = (1000)9 = (103)9 = (10)27 = 10(27-24) = 103 = 1000 1024 1024 1024 | |
| 9. |
How many 3 digit numbers are divisible by 6 in all ? |
| Answer» Required numbers are 102, 108, 114, ... , 996 This is an A.P. in which a = 102, d = 6 and l = 996 Let the number of terms be n. Then, a + (n - 1)d = 996 102 + (n - 1) x 6 = 996 6 x (n - 1) = 894 (n - 1) = 149 n = 150. | |
| 10. |
A 3-digit number 43 is added to another 3-digit number 984 to give a 4-digit number 137, which is divisible by 11. Then, ( + ) = ? |
| Answer» 4 a 3 | 9 8 4 } ==> a + 8 = b ==> b - a = 8 13 b 7 | Also, 13 b7 is divisible by 11 (7 + 3) - (b + 1) = (9 - b) (9 - b) = 0 b = 9 (b = 9 and a = 1) (a + b) = 10. | |
| 11. |
8597 - ? = 7429 - 4358 |
| Answer» 7429 Let 8597 - x = 3071 -4358 Then, x = 8597 - 3071 ---- = 5526 3071 ---- | |
| 12. |
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 ? |
| Answer» Let the number be x and on dividing x by 5, we get k as quotient and 3 as remainder. x = 5k + 3 x2 = (5k + 3)2 = (25k2 + 30k + 9) = 5(5k2 + 6k + 1) + 4 On dividing x2 by 5, we get 4 as remainder. | |
| 13. |
How many 3-digit numbers are completely divisible 6 ? |
| Answer» 3-digit number divisible by 6 are: 102, 108, 114,... , 996 This is an A.P. in which a = 102, d = 6 and l = 996 Let the number of terms be n. Then tn = 996. a + (n - 1)d = 996 102 + (n - 1) x 6 = 996 6 x (n - 1) = 894 (n - 1) = 149 n = 150 Number of terms = 150. | |
| 14. |
How many natural numbers are there between 23 and 100 which are exactly divisible by 6 ? |
| Answer» Required numbers are 24, 30, 36, 42, ..., 96 This is an A.P. in which a = 24, d = 6 and l = 96 Let the number of terms in it be n. Then tn = 96 a + (n - 1)d = 96 24 + (n - 1) x 6 = 96 (n - 1) x 6 = 72 (n - 1) = 12 n = 13 Required number of numbers = 13. | |
| 15. |
The smallest prime number is: |
| Answer» The smallest prime number is 2. | |
| 16. |
(12345679 x 72) = ? |
| Answer» 12345679 x 72 = 12345679 x (70 +2) = 12345679 x 70 + 12345679 x 2 = 864197530 + 24691358 = 888888888 | |
| 17. |
On dividing a number by 357, we get 39 as remainder. On dividing the same number 17, what will be the remainder ? |
| Answer» Let x be the number and y be the quotient. Then, x = 357 x y + 39 = (17 x 21 x y) + (17 x 2) + 5 = 17 x (21y + 2) + 5) Required remainder = 5. | |
| 18. |
If the product 4864 x 9 P 2 is divisible by 12, then the value of P is: |
| Answer» Clearly, 4864 is divisible by 4. So, 9P2 must be divisible by 3. So, (9 + P + 2) must be divisible by 3. P = 1. | |
| 19. |
-84 x 29 + 365 = ? |
| Answer» Given Exp. = -84 x (30 - 1) + 365 = -(84 x 30) + 84 + 365 = -2520 + 449 = -2071 | |
| 20. |
A number when divided by 296 leaves 75 as remainder. When the same number is divided by 37, the remainder will be: |
| Answer» Let x = 296q + 75 = (37 x 8q + 37 x 2) + 1 = 37 (8q + 2) + 1 Thus, when the number is divided by 37, the remainder is 1. | |
| 21. |
397 x 397 + 104 x 104 + 2 x 397 x 104 = ? |
| Answer» Given Exp. = (397)2 + (104)2 + 2 x 397 x 104 = (397 + 104)2 = (501)2 = (500 + 1)2 = (5002) + (1)2 + (2 x 500 x 1) = 250000 + 1 + 1000 = 251001 | |
| 22. |
(35423 + 7164 + 41720) - (317 x 89) = ? |
| Answer» 35423 317 x 89 = 317 x (90 -1 ) + 7164 = (317 x 90 - 317) + 41720 = (28530 - 317) ----- = 28213 84307 - 28213 ----- 56094 ----- | |
| 23. |
In dividing a number by 585, a student employed the method of short division. He divided the number successively by 5, 9 and 13 (factors 585) and got the remainders 4, 8, 12 respectively. If he had divided the number by 585, the remainder would have been |
| Answer» 5 | x z = 13 x 1 + 12 = 25 -------------- 9 | y - 4 y = 9 x z + 8 = 9 x 25 + 8 = 233 -------------- 13| z - 8 x = 5 x y + 4 = 5 x 233 + 4 = 1169 -------------- | 1 -12 585) 1169 (1 585 --- 584 --- Therefore, on dividing the number by 585, remainder = 584. | |
| 24. |
In a division sum, the divisor is 10 times the quotient and 5 times the remainder. If the remainder is 46, what is the dividend ? |
| Answer» Divisor = (5 x 46) = 230 10 x Quotient = 230 = 230 = 23 10 Dividend = (Divisor x Quotient) + Remainder = (230 x 23) + 46 = 5290 + 46 = 5336. | |
| 25. |
4500 x ? = 3375 |
| Answer» 4500 x x = 3375 x = 337575 = 3 4500100 4 | |
| 26. |
What smallest number should be added to 4456 so that the sum is completely divisible by 6 ? |
| Answer» 6) 4456 (742 42 --- 25 24 Therefore, Required number = (6 - 4) = 2. --- 16 12 --- 4 | |
| 27. |
What least number must be subtracted from 13601, so that the remainder is divisible by 87 ? |
| Answer» 87) 13601 (156 87 ---- 490 435 ---- 551 522 --- 29 --- Therefore, the required number = 29. | |
| 28. |
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: |
| Answer» Clearly, (2272 - 875) = 1397, is exactly divisible by N. Now, 1397 = 11 x 127 The required 3-digit number is 127, the sum of whose digits is 10. | |
| 29. |
476 ** 0 is divisible by both 3 and 11. The non-zero digits in the hundred's and ten's places are respectively: |
| Answer» Let the given number be 476 xy 0. Then (4 + 7 + 6 + x + y + 0) = (17 + x + y) must be divisible by 3. And, (0 + x + 7) - (y + 6 + 4) = (x - y -3) must be either 0 or 11. x - y - 3 = 0 y = x - 3 (17 + x + y) = (17 + x + x - 3) = (2x + 14) x= 2 or x = 8. x = 8 and y = 5. | |
| 30. |
If the number 97215 * 6 is completely divisible by 11, then the smallest whole number in place of * will be: |
| Answer» Given number = 97215x6 (6 + 5 + 2 + 9) - (x + 1 + 7) = (14 - x), which must be divisible by 11. x = 3 | |
| 31. |
(11 + 12 + 13 + ... + 20) = ? |
| Answer» (112 + 122 + 132 + ... + 202) = (12 + 22 + 32 + ... + 202) - (12 + 22 + 32 + ... + 102) Ref: (12 + 22 + 32 + ... + n2) = 1 n(n + 1)(2n + 1) 6 = 20 x 21 x 41 - 10 x 11 x 21 6 6 = (2870 - 385) = 2485. | |
| 32. |
If the number 5 * 2 is divisible by 6, then * = ? |
| Answer» 6 = 3 x 2. Clearly, 5 * 2 is divisible by 2. Replace * by x. Then, (5 + x + 2) must be divisible by 3. So, x = 2. | |
| 33. |
A boy multiplied 987 by a certain number and obtained 559981 as his answer. If in the answer both 9 are wrong and the other digits are correct, then the correct answer would be: |
| Answer» 987 = 3 x 7 x 47 So, the required number must be divisible by each one of 3, 7, 47 553681 (Sum of digits = 28, not divisible by 3) 555181 (Sum of digits = 25, not divisible by 3) 555681 is divisible by 3, 7, 47. | |
| 34. |
How many prime numbers are less than 50 ? |
| Answer» Prime numbers less than 50 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47 Their number is 15 | |
| 35. |
( - ) is completely divisible by ( - ), when |
| Answer» For every natural number n, (xn - an) is completely divisible by (x - a). | |
| 36. |
When a number is divided by 13, the remainder is 11. When the same number is divided by 17, then remainder is 9. What is the number ? |
| Answer» x = 13p + 11 and x = 17q + 9 13p + 11 = 17q + 9 17q - 13p = 2 q = 2 + 13p 17 The least value of p for which q = 2 + 13p is a whole number is p = 26 17 x = (13 x 26 + 11) = (338 + 11) = 349 | |
| 37. |
(51 + 52 + 53 + ... + 100) = ? |
| Answer» Sn = (1 + 2 + 3 + ... + 50 + 51 + 52 + ... + 100) - (1 + 2 + 3 + ... + 50) = 100 x (1 + 100) - 50 x (1 + 50) 2 2 = (50 x 101) - (25 x 51) = (5050 - 1275) = 3775. | |
| 38. |
(800 ÷ 64) x (1296 ÷ 36) = ? |
| Answer» Given Exp. = 800 x 1296 = 450 64 36 | |
| 39. |
Which natural number is nearest to 8485, which is completely divisible by 75 ? |
| Answer» On dividing, we get 75) 8485 (113 75 --- 98 75 ---- 235 225 --- 10 --- Required number = (8485 - 10) // Because 10 < (75 - 10) = 8475. | |
| 40. |
If the number 42573 * is exactly divisible by 72, then the minimum value of * is: |
| Answer» 72 = 9 x8, where 9 and 8 are co-prime. The minimum value of x for which 73x for which 73x is divisible by 8 is, x = 6. Sum of digits in 425736 = (4 + 2 + 5 + 7 + 3 + 6) = 27, which is divisible by 9. Required value of * is 6. | |
| 41. |
Which natural number is nearest to 9217, which is completely divisible by 88 ? |
| Answer» On dividing we get, 88) 9217 (104 88 ---- 417 352 ---- 65 ---- Therefore, Required number = 9217 + (88 - 65) // Because (88 - 65) < 65. = 9217 + 23 = 9240. | |
| 42. |
(4300731) - ? = 2535618 |
| Answer» Let 4300731 - x = 2535618 Then x, = 4300731 - 2535618 = 1765113 | |
| 43. |
is a whole number which when divided by 4 gives 3 as remainder. What will be the remainder when 2 is divided by 4 ? |
| Answer» Let n = 4q + 3. Then 2n = 8q + 6 = 4(2q + 1 ) + 2. Thus, when 2n is divided by 4, the remainder is 2. | |
| 44. |
A number when divide by 6 leaves a remainder 3. When the square of the number is divided by 6, the remainder is: |
| Answer» Let x = 6q + 3. Then, x2 = (6q + 3)2 = 36q2 + 36q + 9 = 6(6q2 + 6q + 1) + 3 Thus, when x2 is divided by 6, then remainder = 3. | |
| 45. |
The sum of the two numbers is 12 and their product is 35. What is the sum of the reciprocals of these numbers ? |
| Answer» Let the numbers be a and b. Then, a + b = 12 and ab = 35. a + b = 12 1 + 1 = 12 ab 35 b a 35 Sum of reciprocals of given numbers = 12 35 | |
| 46. |
What will be remainder when 17 is divided by 18 ? |
| Answer» When n is even. (xn - an) is completely divisibly by (x + a) (17200 - 1200) is completely divisible by (17 + 1), i.e., 18. (17200 - 1) is completely divisible by 18. On dividing 17200 by 18, we get 1 as remainder. | |
| 47. |
If 1400 x = 1050. Then, = ? |
| Answer» 1400 x x = 1050 x = 1050 = 3 1400 4 | |
| 48. |
(1 + 2 + 3 + ... + 10) = ? |
| Answer» We know that (12 + 22 + 32 + ... + n2) = 1 n(n + 1)(2n + 1) 6 Putting n = 10, required sum = 1 x 10 x 11 x 21 = 385 6 | |
| 49. |
The sum all even natural numbers between 1 and 31 is: |
| Answer» Required sum = (2 + 4 + 6 + ... + 30) This is an A.P. in which a = 2, d = (4 - 2) = 2 and l = 30. Let the number of terms be n. Then, tn = 30 a + (n - 1)d = 30 2 + (n - 1) x 2 = 30 n - 1 = 14 n = 15 Sn = n (a + l) = 15 x (2 + 30) = 240. 2 2 | |
| 50. |
The difference between the place value and the face value of 6 in the numeral 856973 is |
| Answer» (Place value of 6) - (Face value of 6) = (6000 - 6) = 5994 | |