ankur1901 wrote:
The remainder when 7^84 is divided by 342 is :
1. 0
2. 1
3. 49
4. 341
Dear
ankur1901,
First, let me make perfectly clear: this is NOT a GMAT question. This is far too advanced for anything on the GMAT. This is getting into mathematical hot-shot territory.
Step one is to notice that 342 = 343 -1, and of course, 343 = 7^3, so 342 = (7^3) - 1.
Step two is to remember that (a^n - 1) is divisible by (a^m - 1) if n is divisible by m. Obviously, 84 is divisible by 3. Therefore:
[(7^84) - 1] must be divisible by [(7^3) - 1] = 342
If 342 goes evenly into [(7^84) - 1], then it must divide into (7^84) leaving a remainder of 1.
Does all this make sense?
Mike
_________________
Mike McGarry
Magoosh Test PrepEducation is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)