Which of the following is divisible by the first thousand positive even integer multiples of 101?
(i) 55650000
(ii) 234177623000
(iii)11111111111110000000000000000000000000
Choose the most appropriate option:	A) None	B) i only	C) ii only	D) iii only	E) i, ii and iii
The digits of (iii) add to 13, so (iii) is not divisible by 3, so is not divisible by 3*101, and hence not divisible by the first thousand positive even integer multiples.   A positive integer x is divisible by the first thousand integer multiples of 101 if and only if it is divisible by their least common multiple. There are at least 12 primes greater than 10 but less than 1000 so to be divisible by the first thousand integer multiples of 101 x must be at least 10^12. Consquently, neither (i) not (ii) is divisible by the first thousand integer multiples of 101.   Nonenswer None
<result>A</result>
Which of the following is divisible by the first thousand positive even integer multiples of 101?
(i) 55650000
(ii) 234177623000
(iii)11111111111110000000000000000000000000