How many perfect cubes are there between 1 and 100000 which are divisible by 7?
Show answer & explanation
Correct answer: B
Explanation
The correct option is 2.
A perfect cube that is divisible by 7 ,when that number contain a cube of 7 or a perfect multiple of 7's cube in following form, N = 73 × k3 (where, k = 1, 2, 3.....)
If we, put k = 6 ,then the number become, N = 73 × 63 = 74088.
But, if we put k = 7, then the number become, N = 73 × 73 = 117649.
117649 exceeds 100000, So there are only 6 numbers (when, k =1,2,....,6) present between 1 and 100000 which are divisible by 7.