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If N = 5/6 + 6/7 + 7/8 + 8/9 + 9/10 + 10/11, then which of the followi

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If N = 5/6 + 6/7 + 7/8 + 8/9 + 9/10 + 10/11, then which of the followi [#permalink]

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If N = 5/6 + 6/7 + 7/8 + 8/9 + 9/10 + 10/11, then which of the following must be true of N?

A) 5/6 < N < 10/11

B) 21/10 < N < 9/2

C) 5 < N < 5 1/11

D) 5 < N < 5 5/11

E) 30 < N < 60
[Reveal] Spoiler: OA

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Re: If N = 5/6 + 6/7 + 7/8 + 8/9 + 9/10 + 10/11, then which of the followi [#permalink]

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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.

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Re: If N = 5/6 + 6/7 + 7/8 + 8/9 + 9/10 + 10/11, then which of the followi [#permalink]

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New post 23 Sep 2016, 12:00
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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Re: If N = 5/6 + 6/7 + 7/8 + 8/9 + 9/10 + 10/11, then which of the followi [#permalink]

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\(N = \frac{5}{6} + \frac{6}{7} + \frac{7}{8} + \frac{8}{9} + \frac{9}{10} + \frac{10}{11}\)

\(N = 1 - \frac{1}{6} + 1 - \frac{1}{7} + 1 - \frac{1}{8} + 1 - \frac{1}{9} + 1 - \frac{1}{10} + 1 - \frac{1}{11}\)

\(N = 6 - (\frac{1}{6} + \frac{1}{7} + \frac{1}{8} + \frac{1}{9} + \frac{1}{10} + \frac{1}{11})\)


\(\frac{1}{6} + \frac{1}{7} + \frac{1}{8} + \frac{1}{9} + \frac{1}{10} + \frac{1}{11}\)

Max value of above fraction will be \(\frac{6}{6}\)= 1

Minimum value = \(\frac{6}{11}\)


6-1 <= N <= 6-\(\frac{6}{11}\)

6-1 <= N <= \(\frac{60}{11}\)

6-1 <= N <= 5\(\frac{5}{11}\)

Ans. D
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Re: If N = 5/6 + 6/7 + 7/8 + 8/9 + 9/10 + 10/11, then which of the followi [#permalink]

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Here's another way to do this:

N = 5/6 + 6/7 + 7/8 + 8/9 + 9/10 + 10/11

We should also know that in proper fractions (where numerator < denominator), adding same value to both numerator and denominator increases the value of fraction (eg, if we add 1 to both numerator and denominator of 5/6, we will get (5+1)/(6+1) = 6/7, which will become greater than 5/6).
Hence 5/6 < 6/7 < 7/8 < 8/9 < 9/10 < 10/11

Now if we replace all 6 terms with the smallest term 5/6, of course it will decrease the value of given number N. But still lets see what happens
5/6 + 5/6 + 5/6 + 5/6 + 5/6 + 5/6 = 5/6 * 6 = 5

But N must be more than this (the way we replaced), so N > 5

Now lets replace all 6 terms with the highest term 10/11, this will of course increase the value of N but lets see what happens
10/11 + 10/11 + 10/11 + 10/11 + 10/11 + 10/11 = 10/11 * 6 = 60/11 = 5 5/11

But N must be less than this (the way we replaced), so N < 5 5/11

Combining we get
5 < N < 5 5/11

Hence D answer

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Re: If N = 5/6 + 6/7 + 7/8 + 8/9 + 9/10 + 10/11, then which of the followi   [#permalink] 19 Oct 2017, 10:15
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