3 + 33 + 333 + 3.33 ------ 372.33 ------
❨ | 1 - | 1 | ❩ | + | ❨ | 1 - | 2 | ❩ | + | ❨ | 1 - | 3 | ❩ | + ... up to n terms =? |
n | n | n |
Given sum |
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On dividing, we get 75) 8485 (113 75 --- 98 75 ---- 235 225 --- 10 --- Required number = (8485 - 10) // Because 10 < (75 - 10) = 8475.
So, 9P2 must be divisible by 3. So, (9 + P + 2) must be divisible by 3.
∴ P = 1.
87) 13601 (156 87 ---- 490 435 ---- 551 522 --- 29 --- Therefore, the required number = 29.
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.
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.
60% of | 3 | of x = 36 |
5 |
⟹ | 60 | x | 3 | x x = 36 |
100 | 5 |
⟹ x = | ❨ | 36 x | 25 | ❩ | = 100 |
9 |
∴ Required number = 100
768 x 768 x 768 + 232 x 232 x 232 | =? |
768 x 768 - 768 x 232 + 232 x 232 |
Given Exp. = | (a3 + b3) | = (a + b) = (768 + 232) = 1000 |
(a2 - ab + b2) |
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.
Then x, = 4300731 - 2535618 = 1765113
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