joannaecohen wrote:

Each fraction is close to 1 so we know that the sum will be less than 6. Lets just say they're each 1 so N=6. But now we have to subtract the difference

1/6+1/7+1/8+1/9+1/10+1/11. We can estimate these each as 1/10-->5/10 which is 1/2. D is the closest representation of this.

I think it isn't a matter of which is the "closest" approximation of N because the question asks which one MUST be true.

Therefore the right answer may be even a statement which is not a close approximation of N (it just has to be true), whereas a good approximation of N may be the wrong answer.

as a consequence i belive that the quickest and most certain way to answer this question in by exclusion of the impossible answers.

A) FALSE_____ N<10/11 is impossible because N=10/11+ a lot of other numbers, thus N must be >10/11

B) FALSE_____N<9/2=4.5 is impossible because each of the 6 numbers which constitute N are very close to 1( So it is between 5 and 6 and >4.5)

C)FALSE____ 51/11 <5 , whereas N is clearly >5

D) NO SENSE! because 55/11=5 therefore 5<N<5 is impossible.

E) FALSE_____ N is clearly <30 indeed it is between 5 and 6

In conclusion i think that there are not correct answers.

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