Question

The difference between the cubes of two consecutive numbers is 127.what are the numbers

Answer 1

Lets look at the Cubes...

For consecutive Cubes to have a difference of 127 the numbers(not Cube's) must be Small...

but the cube of the greater number among the consecutive digits must also be greater than 127.

now Keeping this in mind lets look at the cubes of some numbers which fall in this range...

5³=125
6³=216
7³=343
8³=512

here when we check on 7³-6³ = 343-216
we get 127 as the answer...

So to conclude: The required numbers are 7 and 6.

Hope it helps...