What is the remainder when is divided by 100?
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Since 25! has lots of factors of 5 and 2, it should end in at least two zeros, so it's a multiple of 100. Then the answer just depends on 5! = 120, which leaves remainder 20. Is that the intended shortcut?
Yep, that's exactly how I did it. Once you see the 100, check 25! mod 100 first.
Nice, I was trying to compute 25! for way too long before noticing this.
Wait, why is 25! a multiple of 100? I get that there are 5s and 2s, but how do we know there are at least two 10s?
Count the pairs of 2 and 5. There are way more than enough of both, so you get two factors of 10.
Any factorial from 10! onward ends in at least two zeros, and 25! definitely qualifies.
I picked 25 because I thought 25! + 5! had something to do with 25. Rookie mistake, but at least I see why the 100 matters now.
Solid 600-level question. Not hard once you spot the zero trick, but easy to overcomplicate under time pressure.
What it tests
Your fluency with the order of operations, fractions, decimals, and basic number sense — the foundation every quant question leans on.
Common trap
Applying the order of operations out of sequence or rounding intermediate values before the final step.