Financier wrote:
What is the remainder when (18^22)^10 is divided by 7 ?
А 1
B 2
C 3
D 4
E 5
I think this question is beyond the GMAT scope. It can be solved with Fermat's little theorem,
which is not tested on GMAT. Or another way:
(18^{22})^{10}=18^{220}=(14+4)^{220} now if we expand this all terms but the last one will have 14 as multiple and thus will be divisible by 7. The last term will be
4^{220}. So we should find the remainder when
4^{220} is divided by 7.
4^{220}=2^{440}.
2^1 divided by 7 yields remainder of 2;
2^2 divided by 7 yields remainder of 4;
2^3 divided by 7 yields remainder of 1;
2^4 divided by 7 yields remainder of 2;
2^5 divided by 7 yields remainder of 4;
2^6 divided by 7 yields remainder of 1;
...
So the remainder repeats the pattern of 3: 2-4-1. So the remainder of
2^{440} divided by 7 would be the same as
2^2 divided by 7 (440=146*
3+
2).
2^2 divided by 7 yields remainder of 4.
Answer: D.
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47% (02:14) correct
