Find all solutions of .

Question

Find all solutions of  .

Quizplus · Accepted Answer

The given hexadecimal number is in the form of: 
11eb80b1_b0a0_3c55_a291_b16f0fd9f4a0_TB8633_11
We observe that each hexadecimal digit ranges from 0 to F, i.e., 0 to 15 in decimal. 
Adding the last hexadecimal digit to the sum of all the other digits up to the last (TB8633 in this case) takes the modulus by 11. Hence, we can use this property to find the correct option. 
On adding all the digits up to the last (which is TB8633), we get: 
(1+1+e+b+8+0+b+1+b+0+a+0+3+c+5+5+a+2+9+1+b+1+6+f+0+f+d+9+f+4+a+0)
= 118
Adding the last digit, 3, to the above sum, we get: 
(118 + 3) = 121 which is divisible by 11. 
Hence, the correct option is the one with the last digit 9, as adding 9 to 118 makes the sum divisible by 11. 
Option (D) is the only option with the last digit 9.

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