Graduate Management Admission Test (GMAT) Practice Test

The test for divisibility by 11 involves finding the difference between the sum of the digits in the odd positions and the sum of the digits in the even positions of a given number. If the absolute value of this difference is either 0 or a multiple of 11, then the original number is divisible by 11.

For example, consider the number 2728. The digits in the odd positions are 2 (1st position) and 2 (3rd position) while the digits in the even positions are 7 (2nd position) and 8 (4th position). The sum of the odd-positioned digits is 2 + 2 = 4 and the sum of the even-positioned digits is 7 + 8 = 15. The difference between these sums is |4 - 15| = 11, which is a multiple of 11, thereby indicating that 2728 is divisible by 11.

This method of testing for divisibility is unique to 11 and sets it apart from common practices related to divisibility tests for other numbers, such as simply summing all the digits or looking at the last digit.