Interview Q&A / Aptitude

31. What is the remainder when 2^100 is divided by 7?

    The remainder is 2. Since 2^3 = 8 leaves remainder 1 when divided by 7, 2^99 = (2^3)^33 also leaves 1, so 2^100 = 2^99 x 2 leaves 1 x 2 = 2.

    IntermediateQuick answer1 min read
32. What is the rule of 72, and how long does money take to double at 9% compound interest?

    Doubling time is roughly 72 divided by the annual rate in percent. At 9% that is 72 / 9 = 8 years. The exact answer is log 2 / log 1.09, about 8.04 years, so the rule is very close.

    IntermediateQuick answer1 min read
33. Which is the next year after 2025 that will have exactly the same calendar as 2025?

    2031. Two years share a calendar when they start on the same weekday and are both leap or both non-leap. Adding odd days from 2025 onward (1, 1, 1, 2, 1, 1) reaches 7 after 2030, so 2031 starts on the same day as 2025 (Wednesday) and is also a non-leap year.

    IntermediateQuick answer1 min read