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- Question
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
- 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.
- 1. The sum of first 45 natural numbers is:
Options- A. 1035
- B. 1280
- C. 2070
- D. 2140 Discuss
- 2.
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
- 3. 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
- 4. 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
- 5. Which one of the following numbers is completely divisible by 45?
Options- A. 181560
- B. 331145
- C. 202860
- D. 2033555
- E. None of these Discuss
- 6. What is the unit digit in (4137)754?
Options- A. 1
- B. 3
- C. 7
- D. 9 Discuss
- 7. How many 3-digit numbers are completely divisible 6?
Options- A. 149
- B. 150
- C. 151
- D. 166 Discuss
- 8. What is the unit digit in {(6374)1793 x (625)317 x (341491)}?
Options- A. 0
- B. 2
- C. 3
- D. 5 Discuss
- 9. (xn - an) is completely divisible by (x - a), when
Options- A. n is any natural number
- B. n is an even natural number
- C. n is and odd natural number
- D. n is prime Discuss
- 10. (22 + 42 + 62 + ... + 202) =?
Options- A. 770
- B. 1155
- C. 1540
- D. 385 x 385 Discuss
Numbers problems
Search Results
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: 578
Explanation:
| Given Exp. = | (a3 - b3) | = (a - b) = (854 - 276) = 578 |
| (a2 + ab + b2) |
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: 3⁄4
Explanation:
| 1400 x x = 1050 ⟹ x = | 1050 | = | 3 |
| 1400 | 4 |
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.
Correct Answer: 9
Explanation:
Unit digit in (4137) 754 = Unit digit in {[(4137) 4 ] 188 x (4137) 2 }
=Unit digit in { 292915317923361 x 17114769 }
= (1 x 9) = 9
Correct Answer: 150
Explanation:
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.
Correct Answer: 0
Explanation:
Unit digit in (6374) 1793 = Unit digit in (4) 1793
= Unit digit in [(42)896 x 4]
= Unit digit in (6 x 4) = 4
Unit digit in (625)317 = Unit digit in (5)317 = 5
Unit digit in (341)491 = Unit digit in (1)491 = 1
Required digit = Unit digit in (4 x 5 x 1) = 0.
Correct Answer: n is any natural number
Explanation:
For every natural number n , ( x n - a n ) is completely divisible by ( x - a ).
Correct Answer: 1540
Explanation:
(2 2 + 4 2 + 6 2 + ... + 20 2 ) = (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.
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