Multiple choice general knowledge math & puzzles

Z is a set of three digit numbers of base 10 which are divisible by 3 and end with 1 when written in base 5 and base 7 notations, then how many elements does Z has?

  1. 8

  2. 9

  3. 10

  4. 12

Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A number ending in 1 in base 5 and 7 must be of the form 35k + 1. It must also be divisible by 3. Checking 35k+1 for divisibility by 3: k=1 (36), k=4 (141), k=7 (246), etc. In the range 100-999, the values are 141, 246, 351, 456, 561, 666, 771, 876, 981, totaling 9 elements.