Getting into the 3rd round is extremely tough, and downright impossible for the W/H/S schools.
To be honest, I wouldn't bother sending this to any admissions people (I'm assuming that is what you are asking by your forum title). This comment would be viewed as an excuse, however true it is, and they may not even read the rest of your letter.
Quote:
The fact my job is so busy I think I burnt out trying to juggle both study and work, and I sat the GMAT last week and was disappointed with my result - the quant really ruined my score.
Is it possible for you to wait a year and just chip away at the math slowly? I was going to apply this year but FUBAR'd the math section (even though I'm an engineer, grrrrrrrrr) so will spend a long time slowly re-learning the math from the ground up. Maybe a prep class would help you too? That requires you to study at least a minimum amount and could help with motivation. We are all busy people, so unless you are working 16 hours a day, someone has found time to study.