help with fraction please

[ashish1354]

what could be possibly an approach to quickly solve this problem?

[GMATDavid]

Hi,

You don't really have to do the math on this one, if you just think about it logically.

Moving from left to right:

6/7 is a bit bigger than 5/6, so 6/7 - 5/6 will bring us to a small fraction greater than 0. 4/5 is a bit smaller than 5/6, so when we add 4/5 back in, we go above the 1/2 mark but certainly not above 1. 3/4 is a bit smaller than 4/5, so when we subtract 3/4 out we are going back down into small fraction land. 2/3 is smaller than 3/4, so when we add 2/3 back in, we get back up to the more than 1/2 range. 1/2 is less than 2/3, so we are going back down into the smaller fraction area.

Thus, the answer choice is greater than 0 but less than 1/2.

Cheers,