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# Let n be a positive integer such that 1/2 + 1/3 + 1/7 + 1/n is an inte

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Math Expert
Joined: 02 Sep 2009
Posts: 59588
Let n be a positive integer such that 1/2 + 1/3 + 1/7 + 1/n is an inte  [#permalink]

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19 Mar 2019, 00:07
00:00

Difficulty:

15% (low)

Question Stats:

82% (01:39) correct 18% (02:04) wrong based on 95 sessions

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Let n be a positive integer such that 1/2 + 1/3 + 1/7 + 1/n is an integer. Which of the following statements is not true:

(A) 2 divides n

(B) 3 divides n

(C) 6 divides n

(D) 7 divides n

(E) n > 84

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Intern
Joined: 14 Jan 2016
Posts: 9
Location: India
Concentration: Finance, Marketing
Re: Let n be a positive integer such that 1/2 + 1/3 + 1/7 + 1/n is an inte  [#permalink]

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19 Mar 2019, 01:19
lcd of 1/2,1/3 & 1/7 = 2*3*7 = 42

->n must be 42 or its divisor to satisfy the condition
->option E : n>84 is not trye

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Intern
Joined: 15 Aug 2018
Posts: 9
Re: Let n be a positive integer such that 1/2 + 1/3 + 1/7 + 1/n is an inte  [#permalink]

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21 Apr 2019, 21:14
1
Could you please elaborate? I don't understand what's the concept here.
Manager
Joined: 27 Mar 2018
Posts: 79
Location: India
Let n be a positive integer such that 1/2 + 1/3 + 1/7 + 1/n is an inte  [#permalink]

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04 May 2019, 13:08
1
navingr8 wrote:
Could you please elaborate? I don't understand what's the concept here.

This is how I solved it-
$$\frac{1}{2}$$ + $$\frac{1}{3}$$ + $$\frac{1}{7}$$ + $$\frac{1}{n}$$ = $$\frac{41n + 1}{42n}$$

n has to be 1 which satisfies all options except E

Please correct me if there's any issue in my approach.
Let n be a positive integer such that 1/2 + 1/3 + 1/7 + 1/n is an inte   [#permalink] 04 May 2019, 13:08
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