Interview Q&A / Aptitude

1. How many trailing zeros does 250! have?

   62. Each trailing zero needs a pair of 2 and 5, and 5s are scarcer, so count the 5s: 250/5 = 50, 250/25 = 10, 250/125 = 2 (take whole parts), total 62.

   BeginnerQuick answer1 min read
2. What digit x makes the number 4x6723 divisible by 11?

   x = 2. For divisibility by 11, the difference between the sum of digits in odd places and in even places (counted from the right) must be 0 or a multiple of 11. Here that difference is x - 2, so x = 2, giving 426723 = 11 x 38793.

   BeginnerQuick answer1 min read
3. What is the unit digit of 7^95?

   The answer is 3. Unit digits of powers of 7 repeat in a cycle of four (7, 9, 3, 1). 95 leaves remainder 3 when divided by 4, so 7^95 ends like 7^3, which ends in 3.

   BeginnerQuick answer1 min read
4. How many factors does 360 have, and what is the sum of those factors?

   Write 360 = 2^3 x 3^2 x 5. Number of factors = (3+1)(2+1)(1+1) = 24. Sum of factors = (1+2+4+8)(1+3+9)(1+5) = 15 x 13 x 6 = 1170.

   IntermediateQuick answer1 min read
5. 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