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- Question
Which one of the following numbers is completely divisible by 45?
Options- A. 181560
- B. 331145
- C. 202860
- D. 2033555
- E. None of these
- Correct Answer
- 202860
Explanation
45 = 5 x 9, where 5 and 9 are co-primes.Unit digit must be 0 or 5 and sum of digits must be divisible by 9.
Among given numbers, such number is 202860.
- 1. 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) =?
Options- A. 10
- B. 11
- C. 12
- D. 15 Discuss
- 2. 7589 -? = 3434
Options- A. 4242
- B. 4155
- C. 1123
- D. 11023
- E. None of these Discuss
- 3. (4300731) -? = 2535618
Options- A. 1865113
- B. 1775123
- C. 1765113
- D. 1675123
- E. None of these Discuss
- 4. 476 ** 0 is divisible by both 3 and 11. The non-zero digits in the hundred's and ten's places are respectively:
Options- A. 7 and 4
- B. 7 and 5
- C. 8 and 5
- D. None of these Discuss
- 5.
768 x 768 x 768 + 232 x 232 x 232 =? 768 x 768 - 768 x 232 + 232 x 232
Options- A. 1000
- B. 536
- C. 500
- D. 268
- E. None of these Discuss
- 6. If 1400 x x = 1050. Then, x =?
Options- A. 1⁄4
- B. 3⁄5
- C. 2⁄3
- D. 3⁄4
- E. None of these Discuss
- 7. The sum of the two numbers is 12 and their product is 35. What is the sum of the reciprocals of these numbers?
Options- A. 12⁄35
- B. 1⁄35
- C. 35⁄8
- D. 7⁄32 Discuss
- 8.
854 x 854 x 854 - 276 x 276 x 276 =? 854 x 854 + 854 x 276 + 276 x 276
Options- A. 1130
- B. 578
- C. 565
- D. 1156
- E. None of these Discuss
- 9. The sum of first 45 natural numbers is:
Options- A. 1035
- B. 1280
- C. 2070
- D. 2140 Discuss
- 10. n is a whole number which when divided by 4 gives 3 as remainder. What will be the remainder when 2n is divided by 4?
Options- A. 3
- B. 2
- C. 1
- D. 0 Discuss
Numbers problems
Search Results
Correct Answer: 10
Explanation:
4 a 3 | 9 8 4 } ==> a + 8 = b ==> b - a = 8 13 b 7 |Also, 13 b 7 is divisible by 11 ⟹ (7 + 3) - ( b + 1) = (9 - b )
⟹ (9 - b) = 0
⟹ b = 9
∴ (b = 9 and a = 1) ⟹ (a + b) = 10.
Correct Answer: 4155
Explanation:
Let 7589 -x = 3434
Then, x = 7589 - 3434 = 4155
Correct Answer: 1765113
Explanation:
Let 4300731 - x = 2535618
Then x, = 4300731 - 2535618 = 1765113
Correct Answer: 8 and 5
Explanation:
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.
Correct Answer: 1000
Explanation:
| Given Exp. = | (a3 + b3) | = (a + b) = (768 + 232) = 1000 |
| (a2 - ab + b2) |
Correct Answer: 3⁄4
Explanation:
| 1400 x x = 1050 ⟹ x = | 1050 | = | 3 |
| 1400 | 4 |
Correct Answer: 12⁄35
Explanation:
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 |
Correct Answer: 578
Explanation:
| Given Exp. = | (a3 - b3) | = (a - b) = (854 - 276) = 578 |
| (a2 + ab + b2) |
Correct Answer: 1035
Explanation:
Let S n = (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.
Correct Answer: 2
Explanation:
Let n = 4 q + 3. Then 2 n = 8 q + 6 = 4(2 q + 1 ) + 2.
Thus, when 2n is divided by 4, the remainder is 2.
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