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

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Manager
Joined: 08 Sep 2017
Posts: 65
In a certain clothing store, the most expensive pair of socks sells fo  [#permalink]

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09 Sep 2018, 14:22
2
00:00

Difficulty:

55% (hard)

Question Stats:

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

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 _________________ Kudos please if you liked my post Thanks! Senior Manager Joined: 24 Aug 2016 Posts: 311 Location: India Concentration: Entrepreneurship, Operations GMAT 1: 540 Q49 V16 GMAT 2: 640 Q47 V31 GMAT 3: 630 Q48 V28 GPA: 3.4 Re: In a certain clothing store, the most expensive pair of socks sells fo [#permalink] ### Show Tags 09 Sep 2018, 17:41 1 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)
_________________

Please let me know if I am going in wrong direction.
Thanks in appreciation.

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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