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# Each of the 110 residents in Dashville is either a rancher or an tract

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Math Expert
Joined: 02 Sep 2009
Posts: 52438
Each of the 110 residents in Dashville is either a rancher or an tract  [#permalink]

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27 May 2018, 09:15
00:00

Difficulty:

65% (hard)

Question Stats:

58% (02:29) correct 42% (01:50) wrong based on 70 sessions

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Each of the 110 residents in Dashville is either a rancher or an tractor-driver, but not both. How many residents of Dashville are ranchers?

(1) There are more than 81 ranchers who reside in Dashville

(2) The number of ranchers who reside in Dashville is less than three times the number of tractor-drivers who reside in Dashville

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Joined: 24 Aug 2016
Posts: 646
Concentration: Entrepreneurship, Operations
GMAT 1: 630 Q48 V28
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Re: Each of the 110 residents in Dashville is either a rancher or an tract  [#permalink]

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27 May 2018, 18:43
Bunuel wrote:
Each of the 110 residents in Dashville is either a rancher or an tractor-driver, but not both. How many residents of Dashville are ranchers?

(1) There are more than 81 ranchers who reside in Dashville

(2) The number of ranchers who reside in Dashville is less than three times the number of tractor-drivers who reside in Dashville

Say , rancher = r & tractor-driver = t.......r+t=110; r = ?

(1) There are more than 81 ranchers who reside in Dashville ==> r>81 ..r could be anything 82, 83,...etc.... Insufficient.
(2) The number of ranchers who reside in Dashville is less than three times the number of tractor-drivers who reside in Dashville
==> r<3t this condition could be satisfied with a number of ( r,t )pairs (r,t)= (1,109) or (50,60) or (80,30).....etc.... Insufficient.
(1)+(2) ==>
..................... when r = 83 ( as r>81), t =27 ...3t=81<r... donot satisfy 2
..................... when r = 81 , t =29 ...3t=87>r... donot satisfy 1

.....................when r = 82 ( as r>81), t =28 ...3t=84>r....satisfy both cond ..................Thus sufficient.
Hence I would go for option C.
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Please let me know if I am going in wrong direction.
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Joined: 16 Jan 2018
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Re: Each of the 110 residents in Dashville is either a rancher or an tract  [#permalink]

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09 Jun 2018, 20:43
1) clearly insufficient
2) clearly insufficient

1)+2)

if Rancher are 82 then Tractor is 28. (28*3 = 84) . OK
If rancher = 83. then tracteor is 27. (27*3=81). condn 1 violated

only pos soln is 82 and 28. hence C
Re: Each of the 110 residents in Dashville is either a rancher or an tract &nbs [#permalink] 09 Jun 2018, 20:43
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