Hey, I'll do anything for kudos
I am sure there is a fancy/elegant way to solve this question, but on the GMAT, I prefer dirty and reliable that will not result into any confusion and can be done one step at a time.
I would write out all of the possibilities like this:
5 segments: 0.2, 0.4, 0.6, 0.8 or fractions: \(\frac{1}{5}, \frac{2}{5}, \frac{3}{5}, \frac{4}{5}.\)
7 segments: 0.143, 0.286, 0.429, 0.572, 0.715, 0.858 (to find out 0.143 - I am dividing 100 by 7 to the third digit and the multiplying this number by 2, 3, 4, 5, and 6).
You can also do fractions: \(\frac{1}{7}, \frac{2}{7}....\). What I notice immediately is that I will have to convert fractions to common denominators and that's an additional step/pain, so I'd rather stick with decimals.
Decimals are slightly off as it is technically 0.142857, but that should not be material (fingers crossed).
So, looking at the expressions, the least possible difference is between 0.572 and 0.6; (0.4 and 0.429 comes close as well but since the answer choice spread is so large, it does not matter which one you pick).
The difference is 0.0280 (approx) - don't confuse this with 0.280. this is somewhat smaller than \(\frac{1}{30}\), and the number matching that in the answer choices is \(\frac{1}{35}\).
Did I get it?
Edit: this is a longer solution than offered by shaselai - you have to figure out for yourself, which approach is least risky for you (least chance of making an error). Without writing it all out, it would probably take me a bit under a minute to solve it on the GMAT. Then, I would give it another read and cursory check to make sure I did not mess up in my calculations anywhere.
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