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# Let &x be defined such that &x = x + 1/x. The value of &6 + &4 + &2 is

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Math Expert
Joined: 02 Sep 2009
Posts: 52971
Let &x be defined such that &x = x + 1/x. The value of &6 + &4 + &2 is  [#permalink]

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08 Mar 2018, 01:07
00:00

Difficulty:

25% (medium)

Question Stats:

95% (01:40) correct 5% (02:06) wrong based on 64 sessions

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Let &x be defined such that &x = x + 1/x. The value of &6 + &4 + &2 is

(A) 12

(B) 12 7/12

(C) 12 11/12

(D) 13 1/12

(E) 13 5/12

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Math Expert
Joined: 02 Sep 2009
Posts: 52971
Re: Let &x be defined such that &x = x + 1/x. The value of &6 + &4 + &2 is  [#permalink]

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08 Mar 2018, 01:09
Bunuel wrote:
Let &x be defined such that &x = x + 1/x. The value of &6 + &4 + &2 is

(A) 12

(B) 12 7/12

(C) 12 11/12

(D) 13 1/12

(E) 13 5/12

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Re: Let &x be defined such that &x = x + 1/x. The value of &6 + &4 + &2 is  [#permalink]

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08 Mar 2018, 01:17
Bunuel wrote:
Let &x be defined such that &x = x + 1/x. The value of &6 + &4 + &2 is

(A) 12

(B) 12 7/12

(C) 12 11/12

(D) 13 1/12

(E) 13 5/12

As the calculation we're asked to do is straightforward, we'll just do it.
This is a Precise approach.

&6 = 6 + 1/6
&4 = 4 + 1/4
&2 = 2 + 1/2
6+4+2 = 12 and 1/6 + 1/4 + 1/2 = 2/12 + 3/12 + 6/12 = 11/12
(C) 12 11/12 is our answer.
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Joined: 23 Sep 2016
Posts: 213
Re: Let &x be defined such that &x = x + 1/x. The value of &6 + &4 + &2 is  [#permalink]

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08 Mar 2018, 22:40
Bunuel wrote:
Let &x be defined such that &x = x + 1/x. The value of &6 + &4 + &2 is

(A) 12

(B) 12 7/12

(C) 12 11/12

(D) 13 1/12

(E) 13 5/12

IMO C
IF &x = x + 1/x
then &6 + &4 + &2=6+1/6+4+1/4+2+1/2
=155/12
which is C
Intern
Joined: 28 Dec 2017
Posts: 11
Re: Let &x be defined such that &x = x + 1/x. The value of &6 + &4 + &2 is  [#permalink]

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09 Mar 2018, 02:00
&x = x + 1/x. The value of &6 + &4 + &2 is
&6=6+1/6 = 2/2*(6+1/6) (to make it in terms of 12 in denominator )
=6+2/12 = 6 + 1/12 + 1/12
same with &4
&4 = 4+1/4 = 3/3* (4+1/4) = 4 + 1/12 +1/12 +1/12
&2 = 2+1/2 = 6/6* (2+1/2) = 2 +1/12 +1/12 +1/12 +1/12+ 1/12+ 1/12
&6 + &4 + &2 = 6 + 1/12 + 1/12 + 4 + 1/12 +1/12 +1/12 + 3 +1/12 +1/12 +1/12 +1/12
= 6 + 4 + 2 + 1/12+ 1/12+ 1/12+ 1/12+ 1/12+ 1/12+ 1/12+ 1/12+ 1/12+ 1/12+ 1/12
= 12 + 11/12
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Posts: 2827
Re: Let &x be defined such that &x = x + 1/x. The value of &6 + &4 + &2 is  [#permalink]

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12 Mar 2018, 15:27
Bunuel wrote:
Let &x be defined such that &x = x + 1/x. The value of &6 + &4 + &2 is

(A) 12

(B) 12 7/12

(C) 12 11/12

(D) 13 1/12

(E) 13 5/12

&6 + &4 + &2

6 + 1/6 + 4 + 1/4 + 2 + 1/2

12 + 2/12 + 3/12 + 6/12

12 + 11/12

12 11/12

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Re: Let &x be defined such that &x = x + 1/x. The value of &6 + &4 + &2 is   [#permalink] 12 Mar 2018, 15:27
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