Competing against a 10 Speed Bike with 7 Speed bike? I have been cycling for almost about 9 years now. I believe, I have worked myself up to become quite a efficient cyclist. Still, I never felt the need to upgrade my gears to 10 speed, except in races.

Now, here is my recent small story


  A fresher, who just bought a expensive bike with everything the
  modern technology offers, is suddenly bullying a 7 speed bike of mine
  in the race.
  
  Here I am cycling my butt off, with maintaining as much high cadence as I can.
  And there he comes, cycling with a very average cadence without even the
  breaking a sweat and pulling up way ahead of me.


There has to be something like skills or techniques an fairly experienced rider can pull-off to at least become competitive with 10-speeders?
I'm not necessarily sure that the number of gears here is the key issue - it's going to be the upper and lower range: what are the extremes of your gear ratios (or gear inches, if you'd prefer)? 

Maybe your largest gear just isn't large enough. Maybe you need a bigger front cog (or a smaller rear one) to allow you to get up to the same ratio that he can use. 

cadence * gearing = speed


The extra gears on his bike just means the transition between gears is smoother - less of a leap between neighbouring cogs.