quantskillsgmat wrote:find remainder when 7^84 divided by 342
a)1 b)2 c)0 d)49 e)341

7^84 = (7^3)^28 = 343^28

343^28 dividied by 342 gives remainder 1


Option A

Another way to solve this problem, as for many problems like this, is to look for a pattern.

You will notice than when 7 is multipled by 7 (=49) it ends in a 9.. then multiplied by 7 again, the number ends in a 3, then multipled by 7 again the number ends in a 1, multiplied by 7 again the number ends in a 7.. and then the pattern continues - 9, 3, 1, 7 , 9, 3, 1, 7, etc... All we need to know is this ones digit because it will tell us what the remainder will be.

Thus, since 342 ends in a 2, we can test each ones digit from above to find the remainder.. 9/2 = remainder 1, 3/2 = remainder 1, 1/2(doesnt count so move on, 7/2 = remainder 1.. We can see from this that the remainder will be 1

The answer is A

I hope this helps !!

quantskillsgmat wrote:find remainder when 7^84 divided by 342
a)1 b)2 c)0 d)49 e)341

7^3 = 343

Now 343/342 gives 1 as remainder.

Again 7^84 => (7^3)^28/342

So , 343^28/342 =>1