51.
Given exp. = (a² + b² + - ab) = 1 = 1 = 1
(a³ + b³) (a + b) (753 +247) 1000
52. Sum of digits = (5 +1 + 7 + X + 3+ 2 + 4) = (22 + X), which must be divisible by 3.
X=2.
53. Sum of digits = (4 + 8 +1 X + 6 + 7 + 3) = (29 + X), which must be divisible by 9.
X = 7.
54. Given number = 97215X6
(6 + 5 + 2 + 9) – (X + 1 + 7) = (14 – X), which must be divisible by 11.
X = 7.
55. The number 6X2 must be divisible by 8.
(X =3, as 632 is divisible by 8.
56. 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.
57. 99 = 11 x 9 where 11 and 9 are co-primes.
By hit and trial, we find that 114345 is divisible by 11 as well as 9. So, it is divisible by 99.
58. 72 = 9 x 8, where 9 and 8 are co-prime
The minimum value of x for which 73 x is divisible by 8 is, X = 6.
Sum of digits in 425736 = (4 _ 2 + 5 + 7 + 3 + 6) = 27, which is divisible by 9.
Required value of * is 6.
59. 80 = 2 x 5 x 8.
Since 653 Xy is divisible by 2 and 5 both, so Y= 0.
Now, 653 X0 is divisible by 8, so 3X0 should be divisible by 8. This happens when X =2 .
X + y =(2 +|0) = 2.
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