Numbers problems
- 1. The largest 4 digit number exactly divisible by 88 is:
Options- A. 9944
- B. 9768
- C. 9988
- D. 8888
- E. None of these Discuss
Correct Answer: 9944
Explanation:
Largest 4-digit number = 9999
88) 9999 (113
88
----
119
88
----
319
264
---
55
---
Required number = (9999 - 55)
= 9944.
- 2. Which one of the following is a prime number?
Options- A. 161
- B. 221
- C. 373
- D. 437
- E. None of these Discuss
Correct Answer: 373
Explanation:
√437 > 22
All prime numbers less than 22 are : 2, 3, 5, 7, 11, 13, 17, 19.
161 is divisible by 7, and 221 is divisible by 13.
373 is not divisible by any of the above prime numbers.
∴373 is prime.
- 3. 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?
Options- A. 0
- B. 12
- C. 13
- D. 20 Discuss
Correct Answer: 20
Explanation:
Number = (12 x 35)
Correct Quotient = 420 ? 21 = 20
- 4. On dividing a number by 357, we get 39 as remainder. On dividing the same number 17, what will be the remainder?
Options- A. 0
- B. 3
- C. 5
- D. 11 Discuss
Correct Answer: 5
Explanation:
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.
- 5. 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?
Options- A. 4236
- B. 4306
- C. 4336
- D. 5336
- E. None of these Discuss
Correct Answer: 5336
Explanation:
Divisor = (5 x 46) = 230
| ∴ 10 x Quotient = 230 ⟹ = | 230 | = 23 |
| 10 |
Dividend = (Divisor x Quotient) + Remainder
= (230 x 23) + 46
= 5290 + 46
= 5336.
- 6. What is the unit digit in 7105?
Options- A. 1
- B. 5
- C. 7
- D. 9 Discuss
Correct Answer: 7
Explanation:
Unit digit in 7 105 = Unit digit in [ (7 4 ) 26 x 7 ]
But, unit digit in (74)26 = 1
∴ Unit digit in 7105 = (1 x 7) = 7
- 7. (1000)9? 1024 =?
Options- A. 10000
- B. 1000
- C. 100
- D. 10
- E. None of these Discuss
Correct Answer: 1000
Explanation:
| Given Exp. = | (1000)9 | = | (103)9 | = | (10)27 | = 10(27-24) = 103 = 1000 |
| 1024 | 1024 | 1024 |
- 8. 106 x 106 - 94 x 94 =?
Options- A. 2400
- B. 2000
- C. 1904
- D. 1906
- E. None of these Discuss
Correct Answer: 2400
Explanation:
| 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. |
- 9. (112 x 54) =?
Options- A. 67000
- B. 70000
- C. 76500
- D. 77200 Discuss
Correct Answer: 70000
Explanation:
| (112 x 54) = 112 x | ❨ | 10 | ❩ | 4 | = | 112 x 104 | = | 1120000 | = 70000 |
| 2 | 24 | 16 |
- 10. 587 x 999 =?
Options- A. 586413
- B. 587523
- C. 614823
- D. 615173 Discuss
Correct Answer: 586413
Explanation:
| 587 x 999 | = 587 x (1000 - 1) |
| = 587 x 1000 - 587 x 1 | |
| = 587000 - 587 | |
| = 586413. |
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