This is a good question that unfortunately does not have an easy answer. The schools look at many factors and the GMAT score is just one of them. Two of the most critical factors the admissions committees examine in conjunction with the GMAT are the applicant’s:
1. Demographic group and
2. Academic accomplishments
The only factor within your control is the academic accomplishments. (You can always build an ‘alternate transcript’.) Clearly if your GMAT math percentile is abysmal but you graduated valedictorian from the nuclear engineering program at MIT, the admissions committees will be far more likely to assume the GMAT score is not an accurate reflection on your ability to handle their school’s curriculum than if you have the same GMAT score but a 2.5 GPA from a not-so-challenging liberal arts program.
A huge ‘wow’ factor in your application story is also helpful although the admissions committees still want assurances you will be able to handle their curriculum. (In their eyes, there is no point in admitting an applicant who single handedly saved a third-world village from famine if he/she lacks the ability to handle the coursework.)
As a very general rule, you should not feel discouraged from applying to a b-school if your academic accomplishments are good, you have a decent story to tell, and your GMAT is within 50 or 60 points of the average for your demographic group.
Finally, of the schools that you listed above, Columbia is the least lenient towards low GMAT score applicants and Wharton is the second least lenient.