What is log(student wealth) / log(Bill Gates wealth) ?

  • A: 1/1000
  • B: 1/10
  • C: 1/5
  • D: 1/3
  • E: 1/2

    Answer: D

    A good way to approach this question is to take the log2, i.e. find the number of bits required to represent the number.

    We use our rule that 1000 ≅ 10 bits.

    Assume that a student has $8,000 and Bill Gates has $50,000,000,000. Representing student wealth requires 13 bits: 10 bits for 1,000 and 3 bits for 8 (23 = 8). Representing Bill Gates' wealth requires 36 bits: 3 * 10 bits for 1,000,000,000 and 6 bits for 50 (26 = 64).

    Thus, in terms of log2, a student has a bit more than 1/3 of what Bill Gates has.

    It is also easy to do this problem by counting digits in decimal: $8,000 is 4 digits, while $50,000,000,000 is 11 digits. 4 is a bit more than 1/3 of 11.

    The lesson: log grows very slowly.

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