OK, firstly this is not my bike but a friends.

It is a cheap X-Mart/Halfords bike. I cannot remember the number of gears, but I am going to say 24 just so I can identify the issue.

She told me that when she is riding, she gets a ticking noise when she selects 7th. On questioning her she told me she only uses the smallest 3 or 4 rear cogs with the large and middle chain rings, never with the smallest. So I could rule out cross chaining.

I turned the bike over, resting it on saddle and handlebars, popped it into large front and small rear(8th), everything seemed fine, moved the shifter to 7th and the dérailleur shifted, but not sufficiently to change gear, hence the clicking. Moving the shifter up to 6th caused the chain to engage 6th skipping 7th altogether. The rest of the gears seem fine.

I haven't taken it apart - but on a close inspection to my untrained eye it appeared as if the gap between all the gears up to 7 was narrower than the gap between 7 & 8. Could this be possible? Could the last gear have been put on back to front and then the limit screw adjusted to make it work - or am I seeing things and the problem lies not with the perceived gap between the gears but rather a calibration or other issue?

If the cassette is lose (if that thing has a cassette tho) u can have that problem. never trusted those bikes so the next option IMO could be that the spacers are wrong??

My next option thinking that the cassette is ok, then maybe a friction problem somewhere?? If you know how to set up a RD then sure u can figure it out how to fix the cable it might have a kink somewhere.

Good luck

CC, Measure the spacing with a drill bit 120 degrees apart to determine spacing and whether or not the gear is bent. Generally I've found this issue to be with the cable friction.

Brad

Cheers for the input guys, I must say that the grip shifts on her bike seem, to me at least, incredibly stiff. Butthen I have never used grip shifts and try to avoid wherever possible.

when you say measure with bit 120o apart, do you mean at 3 points around the circumference of the gear?

Yes.

Brad

IF it has really cheap components, that type of shifting may be the norm. Basically a problem of too much slack in the mech.

Try riding the bike and shifting from the largest cog to smaller ones.
You may have the same problem.
1st click nothing.
Next click.....3rd.

Could be the rear mech isn't adjusted. When I swapped out the cassette on my bike I had a clicking in higher gears, along with the chain skipping in some gears, jumping others completely and the like. It took me a while to adjust everything (I'd never done it before) but once it was sorted out everything worked perfectly.

First step is to go through proper derailleur adjustment from start to finish (Park tool site and Sheldon's site good for that) especially checking the outer limit screw and cable friction, as both may prevent shifting fully to the small cog. If you loosen the cable completely and shift up to the next cog and then back to the small OK, then the problem is the cable. If it still shifts poorly most likely cause is outer limit screw. If you go through the entire derailleur adjustment procedure and only the high gear is not centered then perhaps the cassette is not right.