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henilshaht
- Junior | Next Rank: 30 Posts
- Posts: 18
- Joined: Mon Sep 30, 2019 5:04 pm
$$\frac{^{6^{35}\ -\ 6^{25}\ -\ 2}}{6}$$
A. 0
B. 1
C. 2
D. 3
E. 4[/list]
A. 0
B. 1
C. 2
D. 3
E. 4[/list]
Hi henilshaht,
We're asked for the remainder when (6^35 - 6^25 - 2) is divided by 6. This is a great 'concept question', meaning that you don't actually have to do much math if you recognize the concepts involved.
To start, the GMAT will NEVER expect you to calculate that type of large value by hand, so that is NOT what this question requires.
Since we're dividing a number by 6, the only possible values for the remainder are 0, 1, 2, 3, 4 and 5. If you increase the numerator by 1, then the remainder will increase by 1 (the exception being that if the current remainder is 5, then increasing the numerator by 1 will 'cycle' the 5 back to a 0). In that same way, if you decrease the numerator by 1, then the remainder will decrease by 1 (again, the exception being if the current remainder is already 0, then it will 'cycle' the 0 to a 5).
Both 6^35 and 6^25 are MULTIPLES of 6... so dividing either of those individual numbers by 6 will give you a remainder of 0. Subtracting a multiple of 6 from a larger multiple of 6 will result in a number that is ALSO a multiple of 6... so whatever 6^35 and 6^25 actually are... the calculation (6^35 - 6^25) IS a multiple of 6.... meaning that the remainder would be 0 if there was no other math to consider.
However, that extra "-2" means that the remainder will no longer be 0. We have to 'cycle' that 0 down "2 spots" ... and the remainder will become 4.
Final Answer: E
GMAT assassins aren't born, they're made,
Rich
