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# If n is a positive integer, is 1/n - 1/(n+1) <0.05? (1) n is odd (2

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Joined: 02 Sep 2009
Posts: 51215
If n is a positive integer, is 1/n - 1/(n+1) <0.05? (1) n is odd (2  [#permalink]

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01 Aug 2018, 04:16
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25% (medium)

Question Stats:

73% (01:52) correct 27% (01:23) wrong based on 67 sessions

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If n is a positive integer, is $$\frac{1}{n} - \frac{1}{n+1} <0.05$$?

(1) n is odd

(2) n is a positive multiple of 7

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Re: If n is a positive integer, is 1/n - 1/(n+1) <0.05? (1) n is odd (2  [#permalink]

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01 Aug 2018, 04:40
Statement 1:
N = 1
N+1 = 2
1/(n(n+1)) = 1/2 < 0.05 (false)
Or
N=19
N+1=20
1/(n(n+1)) = 1/380 < 0.05 (true)
Insufficient.

Statement 2:
N is a positive multiple of 7.
Lowest value of n can be assumed to be N=7
N+1=8
1/(n(n+1)) = 1/56 < 0.05 (true)
Sufficient

Hence B

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Re: If n is a positive integer, is 1/n - 1/(n+1) <0.05? (1) n is odd (2  [#permalink]

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01 Aug 2018, 04:53
Bunuel wrote:
If n is a positive integer, is $$\frac{1}{n} - \frac{1}{n+1} <0.05$$?

​1 / n - 1 / (n+1) < 0.05
(n + 1 - n) / n(n+1) < 0.05
1 / n(n+1) < 0.05
1 / n(n+1) < 1 / 20
n(n+1) > 20 -- A)

(1) n is odd
Plugging values in n(n+1) > 20, multiple values both less than and greater than 20 are possible
Insufficient

(2) n is a positive multiple of 7
Plugging values in n(n+1) > 20
7 * (7+1) = 7 * 8 > 20
Since the least value obtained is greater than 20, its is always greater than 20
Sufficient

Hence, B.
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Re: If n is a positive integer, is 1/n - 1/(n+1) <0.05? (1) n is odd (2  [#permalink]

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01 Aug 2018, 05:07
Bunuel wrote:
If n is a positive integer, is $$\frac{1}{n} - \frac{1}{n+1} <0.05$$?

(1) n is odd

(2) n is a positive multiple of 7

OA: B
n>0, n is an integer
Is $$\frac{1}{n} - \frac{1}{n+1} <0.05$$
Simplifying the question stem
$$\frac{1}{n} - \frac{1}{n+1} <0.05$$
$$\frac{(n+1)-(n)}{n(n+1)}< \frac{5}{100}$$
$$\frac{1}{n(n+1)}< \frac{1}{20}$$
As $$n$$ is positive, multiplying both sides by $$20n(n+1)$$, we get
$$20<n(n+1)$$
$$n(n+1)-20>0$$
$$n^2+n-20>0$$
$$(n+5)(n-4)>0$$
This leads to $$n<-5$$ or $$n>4.$$
as n is positive,Question stem reduces to Is n>4?

Statement 1: n is odd
For n=1,3
Is n>4? : No
For n =5,7,9......
Is n>4? : Yes
Statement 1 alone is insufficient

Statement 2 :n is a positive multiple of 7
Minimum value of n is 7, as it is first positive multiple of 7
Is n>4? : Yes
Statement 2 alone is sufficient
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Joined: 23 Aug 2017
Posts: 26
Re: If n is a positive integer, is 1/n - 1/(n+1) <0.05? (1) n is odd (2  [#permalink]

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01 Aug 2018, 12:44
Bunuel wrote:
If n is a positive integer, is $$\frac{1}{n} - \frac{1}{n+1} <0.05$$?

(1) n is odd

(2) n is a positive multiple of 7

Simplifying the stem:
$$\frac{1}{n} - \frac{1}{n+1} <0.05$$
$$\frac{1}{n(n+1)} < \frac{5}{100}$$
$$\frac{100}{n(n+1)} < 5$$

1) Not possible to solve only konwing N is odd or even. Not sufficient.
2) If we replaced N for any multiple of 7 the result will always be less than 5. Sufficient.

Option B.
Re: If n is a positive integer, is 1/n - 1/(n+1) <0.05? (1) n is odd (2 &nbs [#permalink] 01 Aug 2018, 12:44
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