The sum of all the digits of the positive integer q is equal to the three-digit number x13. If , what is the value of n?
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This is brutal. I see 10^n - 49 and immediately think 10^n - 50 + 1, but I'm stuck. Anyone have a hint that doesn't give away the answer?
Try writing it as (10^n - 50) + 1. What does 10^n - 50 look like?
Also, the digit sum is x13, a three-digit number. That means q has a lot of digits.
I got n=26 but I'm not sure. Can someone confirm if the digit sum x13 works out? I don't want to post spoilers.
Check your digit sum for that n. If it's x13, then x must be a digit. Does it work?
The tricky part is the borrow when subtracting 49 from 10^n. Most people mess that up. After you get q, sum the digits, set equal to x13, and solve for n. It's a 705-805 for a reason.
What it tests
Your grasp of exponent rules — multiplying and dividing powers, power-of-a-power, and negative/zero exponents.
Common trap
Adding exponents when multiplying bases that have the same exponent, or confusing (x^a)^b with x^(a·b).