bb
I have a feeling there is a quirky formula or solution to this question but I don’t know if this is tested on the GMAT….
Bunuel chetan2u - is this a gmat concept question?
bb,
There are various formulas when it comes to remainder:, Fermat’s remainder theorem, Chinese remainder theorem. Luckily, GMAT doesn’t test them.
Having said that, I believe remainder questions can almost always be solved with pattern. If a question can be answered through a formula, I am sure it must be following some pattern.
Here too it should be the case:
2^1:2,
2^2: 4,
2^3: 8,
2^4: 16,
2^5: 32,
2^6: 64,
2^7: 128 or 128-89 or 39,
2^8: 39*2 or 78
2^9: 78*2-89 or 156-89 or 67
2^10: 67*2-89 or 134-89 or 45
2^11: 45*2 or 90-89 or 1
2^12: 1*2 or 2
So, we are repeating the remainders now and there are 11 different remainders in a pattern.
89=11*8+1
So, 2^89 will have same remainder as 2^1 or 2.
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