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.
2056 x 987 | = 2056 x (1000 - 13) |
= 2056 x 1000 - 2056 x 13 | |
= 2056000 - 26728 | |
= 2029272. |
Given Exp. = | 800 | x | 1296 | = 450 |
64 | 36 |
3897 x 999 | = 3897 x (1000 - 1) |
= 3897 x 1000 - 3897 x 1 | |
= 3897000 - 3897 | |
= 3893103. |
So, 9P2 must be divisible by 3. So, (9 + P + 2) must be divisible by 3.
∴ P = 1.
On dividing, we get 75) 8485 (113 75 --- 98 75 ---- 235 225 --- 10 --- Required number = (8485 - 10) // Because 10 < (75 - 10) = 8475.
❨ | 1 - | 1 | ❩ | + | ❨ | 1 - | 2 | ❩ | + | ❨ | 1 - | 3 | ❩ | + ... up to n terms =? |
n | n | n |
Given sum |
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3 + 33 + 333 + 3.33 ------ 372.33 ------
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.
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