Remainder

Hi, there. I'm happy to help with this.

Prompt: When the positive integer n is divided by 25, the remainder is 13. What is the value of 13?

So, we know n/25 = Q + 13/25, or n = Q*25 + 13, where Q, the quotient, can be any positive integer. This means, candidates for n include
25 + 13 = 38
50 + 13 = 63
75 + 13 = 88
100 + 13 = 113
125 + 13 = 138
150 + 13 = 163
175 + 13 = 188 etc. etc.

Statement #1: n < 100

That leaves candidates 38, 63, and 88, so we can't determine a unique value for n. Statement #1, by itself, is insufficient.

Statement #2: When n is divided by 20, the remainder is 3

That leaves candidates 63, 163, 263, 363, etc., so we can't determine a unique value for n. Statement #2, by itself, is insufficient.

Both Statements Combined:
The only number that simultaneously satisfies both statements is n = 63. With combined statements, we are able to determine a unique and definitive numerical answer for the prompt. Combined, the statements are sufficient.

Answer = C

Does this make sense? Here's a related DS question:

https://gmat.magoosh.com/questions/873

Let me know if you have any further questions.

Mike