GMATPrep - number line

allenkt wrote:This one seemed easy but apparently not. The only solution I can think of is in the wording. I answered 2/35 because that is the distance from one tick mark to the next. But since they technically said "between" any of the two tick marks does that mean they are looking for a point that would be equidistant from both tick marks? That is the only way I can see getting 1/35.

.. the q asks for the least distance between any of the two ticks ...

one way u can approach the problem is to consider the number line to be from 0 to 35 ... that is u are increasing it by a factor of 35 ...

... now the distance between the ticks(let us call these the red ticks) that divide the number line into 5 parts is 7 ... and the ticks( and these will be the blue ticks) that divides the line into 7 parts is 5 ... so the least distance between any two lines is the distance between the 2nd red tick which will be at 14 and the 3rd blue tick which will be at 15 ... and the distance between them is 1 ... but since we hace scaled the number line with a factor of 35 .. we will have to divide 1 by 35 to get the original answer ... which is 1/35 .. hope this helps

I don't know if there is an easier way to solve this question. Since 1 units is divided into 5 and 7 equal parts each, the markings will appear as 1/5, 2/5, 3/5, 4/5 and 5/5 (when into 5 equal parts) and appear as 1/7, 2/7, 3/7, 4/7, 5/7, 6/7 and 7/7 (when divided into 7 equal parts).
Difference between 1/5 and 1/7 = 1/5 - 1/7 = (7-5)/35 = 2/35...hence we can quickly eliminate 1/7 and and 1/12 as an option, which cease to stay
It can't be 1/70 (the LCM is 35 for 3&5)....3/7 - 2/5 = 1/35 Hence it's 1/35