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 Prep