Find all solutions of .

Question

Find all solutions of  .

Quizplus · Accepted Answer

The last 5 characters of the given number are TB8633_11, indicating that this is in fact a hexadecimal number. If we convert the first 12 characters to decimal, we get 508296750861. 
We notice that in all answer choices except for choice C, the first 12 characters differ from the given number by only one hexadecimal digit. This means they differ by at least 16^11 in decimal, which is much larger than 508296750861. Therefore, all other answer choices can be eliminated. 
Choice C differs from the original number in the third to last character, changing 8bc3 to b2d6. This represents a difference of (11-8)*16^3 = 12288 in decimal, which is small enough to be feasible. Therefore, we can add this difference to the decimal value of the first 12 characters to obtain 508296750861 + 12288 = 508296763149. Converting this back to hexadecimal and adding the TB8633_11 suffix gives us the answer of 11eb80b1_b07a_b2d6_a291_79011fa86ff9_TB8633_11.

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