Every time Tony Stark makes a suit, he can cut 10% of the time it took for the last suit. Given the time it takes to make the first suit, how long does it take to make 100 suits?
(A) 1 second (B) 2 (C) 3 (D) 4 (E) 5
The answers are 100, 190, 271, 344, and 407 seconds. I don't see how these answers make sense... are they wrong?

Question

Every time Tony Stark makes a suit, he can cut 10% of the time it took for the last suit. Given the time it takes to make the first suit, how long does it take to make 100 suits?
(A) 1 second (B) 2 (C) 3 (D) 4 (E) 5
The answers are 100, 190, 271, 344, and 407 seconds. I don't see how these answers make sense... are they wrong?

anonymous · Answer

This is the sum of a geometric series. Have you covered those?

anonymous · Answer

Upon reading more carefully, the answers do appear to be wrong!

anonymous · Answer

Either way, can you see what you should be doing here?

anonymous · Answer

Is it this?$$100\sum_{1}^{n}0.9^{i-1}$$

anonymous · Answer

I'm not sure what you're trying to do with your notation there ^^;

anonymous · Answer

That seems to give the right answer, but I don't think it applies to the question correctly.

anonymous · Answer

If we take n to be the time to make the first suit,
$$n\sum_{i=1}^{100}0.9^{i-1} = n\sum_{i=0}^{99}0.9^i = \frac{n(1-0.9^{99})}{1-0.9} = 10n(1-0.9^{99}) \approx 10n$$
Which is definitely not in line with the answers. As expected we also see a linear relationship between the initial time and the total time which isn't represented in the answers.

I just realized what you meant with your summation (omitting the i= really shouldn't have tripped me up ^^;). Does that give the correct answer in multiple cases?

anonymous · Answer

Something like "Given that the time it takes to make the first suit is 100 seconds, how long does it take to make n suits? a) 1 etc etc" seems to fit what you get, so I can only assume that's what was intended. Makes a hell of a lot more sense than being able to make his first suit in a second, too.

Maybe the question setter just got excited about Iron Man for a moment~ ^_^

I'd answer the question you've been asked though :p

anonymous · Answer

I brute-forced it in Java and got answers very slightly below 10, 20, 30, 40, and 50, which is in line with your logic. I'll bring all this up with the question-setter, thanks. By the way, this was one of the simpler problems from a high school programming competition (the 5 cases above were just sample cases, the number of suits and initial time were not set) and I got 10n but it was apparently wrong and I figured they screwed up when I saw the actual answers.

anonymous · Answer

Ah, that makes sense. =)