What is the explanation of this question? I individually divided each term by 5 and then added the remainders but the answer was wrong. Can some one please let me know how to solve this?

GRE Quant Problem Solving
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I know it is hard to follow the instructions but can you please give it a try at-least once and reformat your question.

Instructions: https://forums.gregmat.com/t/how-to-ask-better-gre-questions-on-forums/42910

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So to get the remainder, you can take the remainder of each and add them. You actually have two problems here.

(16^16)/5 + (19^19)/5
If you don’t believe this consider (12/5). We can rewrite 12 as (10 + 2)/5. The first is remainder 0 and the second has remainder 2. And that’s the same as the remainder of 12/5 = 2.

Now you can apply the remainder principle
16^1/5 R= 1
16^2/5 R= 1
16^3/5 R= 1
16^4/5 R=1

19/5 R=1
1919/5 R=1
191919/5 R=4
19191919/5 R= 1

So you have 1 + 4 = 5 But 5 is too big. You know you have a 5 and that means the Remainder is ZERO. This is a very tricky problem. It’s going to throw you because you think the first one is giving you 1 and 1 and 1 and 1, when will it ever stop. And then the second one is 1, and 1, and 4, and back to 1. The other tricky part is to see that the total is 1 + 4 = 5 and so the remainder is 0.