✔ 最佳答案
Let x be the no.
1. When rounded off to 2 significant figures, it's divisible by 11.
If it is divisible by 11, the first two digits of the rounded off no. must be equal, i.e.
11, 22, 33, 44, 55, 66, 77, 88, 99.
Since it is greater than 9000, the first two digits of the rounded off no. = 99.
Hence, 9850 <= x <= 9949 --------------------------------------------------(1)
2. When rounded off to 3 significant figures, it's divisible by 4. --------------(2)
To satisfy (1) and (2), the first three digits of the rounded off no. should be
986, 988, 990, 992, 994 --------------------------------------------------(3)
Hence, 9855 <= x <= 9944 ---------------------------------------------------(4)
3. It's divisible by 13. --------------------------------------------------(5)
To satisfy (4) & (5), the possible values of x are
9867, 9880, 9893, 9906, 9919, 9932 -----------------------------------------------(6)
Further to (6), since x is odd, the possible values of x are
9867, 9893, 9919 ------------------------------------------------(7)
Further to (7), to satisfy (3), the only possible value of x = 9919