gmattester wrote:discreet wrote:I think we can generalize this....the Lowest distance should be the GCD\HCF of the two numbers 5 and 7 = 35...
So,lowest possible distance is 1/35....you can test it with any no. of options to satisfy yrself and then perform the test that drholmer has given

....eg: 2 and 5 parts , 6 and 7 parts, 3 and 4 parts etc etc

Can someone verify this method...
Or if someone has shorter method to solve this question with proper logic
It's not likely you'll see this exact type of question again, but the method is correct, although discreet surely means the LCM, not the GCD. I'll only prove it if someone asks, though; the proof is a bit abstract. On the GMAT, you would not be expected to know this kind of fact- for this question, it's easy enough to write down all of the fractions with a common denominator, 35:
5/35, 7/35, 10/35, 14/35, 15/35, 20/35, 21/35, 25/35, 28/35, 30/35
and you can see all the possible distances that way.
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