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In a certain clothing store, the most expensive pair of socks sells fo

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Manager
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Joined: 08 Sep 2017
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In a certain clothing store, the most expensive pair of socks sells fo  [#permalink]

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New post 09 Sep 2018, 14:22
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Difficulty:

  55% (hard)

Question Stats:

63% (03:29) correct 38% (03:02) wrong based on 24 sessions

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In a certain clothing store, the most expensive pair of socks sells for one dollar less than twice the price of the cheapest pair of socks. A customer notices that for exactly $18, she can buy three fewer pairs of the most expensive socks than the cheapest socks. What could be the number of pairs of the cheapest socks she could have purchased?

(A) 3
(B) 5
(C) 6
(D) 12
(E) 36

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Joined: 24 Aug 2016
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Location: India
Concentration: Entrepreneurship, Operations
GMAT 1: 540 Q49 V16
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Re: In a certain clothing store, the most expensive pair of socks sells fo  [#permalink]

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New post 09 Sep 2018, 17:41
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dimmak wrote:
In a certain clothing store, the most expensive pair of socks sells for one dollar less than twice the price of the cheapest pair of socks. A customer notices that for exactly $18, she can buy three fewer pairs of the most expensive socks than the cheapest socks. What could be the number of pairs of the cheapest socks she could have purchased?

(A) 3
(B) 5
(C) 6
(D) 12
(E) 36


Let the Price of Cheapest pair is x . Hence price of expensive pair is 2x-1
For $18 , we get n cheapest pair & N expensive pair . Hence , n=18/x & N=18/(2x-1)
As per the Q steam : \(n-N=3\)
i.e., 18/x - 18/(2x-1) =3
or, 6/x - 6/(2x-1) =1
or , \(6(2x-1)-6x=x(2x-1)\)
or ,\(2x^2 - 7x +6 =0\)
or, \((2x-3)(x-2)=0\) =====> \(x=2,1.5\)

When x=2, 2x-1=3 , n=9 & N=6
When x=1.5, 2x-1=2 , n=12 & N=9.......................Hence the ans is 12 (D)
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Re: In a certain clothing store, the most expensive pair of socks sells fo &nbs [#permalink] 09 Sep 2018, 17:41
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