If n is an integer greater than 6, which of the following must be divisible by 3?
2 Explanations
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Cydney Seigerman, Magoosh Tutor
Hi Sneha :)
Great question! Yes, in the problem, the phrase "integers greater than 6" does all integers (2-digit numbers, 3-digit numbers, etc.) that are larger than 6. However, we can classify all of these integers into three different cases based on their remainder when divided by 3:
Case 1: Integers that have a remainder of 2 when divided by 3.
Case 2: Integers that have a remainder of 1 when divided by 3.
Case 3: Integers that have a remainder of 0 when divided by 3.
Each of the three numbers used in the explanation video reflect one of the cases:
Case 1: 8 --> 8/3 = 2r2
Case 2: 7 --> 7/3 = 2r1
Case 3: 9 --> 9/3 = 3r0
All other integers greater than 6 will fall into one of these cases and will therefore exhibit the same divisibility characteristics of their 1-digit counterparts. So we can limit our discussion in this problem to the three numbers listed above, simplifying the problem and allowing us to determine the correction solution faster :)
2 Explanations