Hi All,
We’re told that K is an integer and that (.0025)(.025)(.00025)(10^K) is an INTEGER. We’re asked for the least possible value of K. Since we’re given a lot of numbers to work with, this is essentially just an Arithmetic question – but you might find the work much faster to deal with depending on how you write-out the given information.
Based on how ‘spread out’ the Answers are written, there’s actually a great short-cut build into this prompt. Since we’re multiplying three fractional values together, that product will be a much smaller positive fraction. There’s no way to make (10^K) equal 0, so that piece of the product has to ‘offset’ all of the decimal places that would occur from multiplying those 3 fractional values together. Even without physically counting them up, we can see that there are a LOT of decimal places there – so there’s only one answer that could reasonably turn the overall product into an integer. If you count up the decimals, you’ll notice that there are 12 decimal places, which will also point you to the correct answer.
Barring those shortcuts, you could visualize the math by writing those decimals as fractions:
25/100 = .25
25/1000 = .025
25/10000 = .0025
Etc.
So we would have:
(25/10,000)(25/1,000)(25/100,000)(10^K)
We need to offset all 3 of those denominators, so that would require that we multiply by 10^4, 10^3 and 10^5, respectively… for a total of 10^12.
Final Answer:
GMAT Assassins aren’t born, they’re made,
Rich