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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
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In a certain clothing store, the most expensive pair of socks sells fo
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28 Jul 2021, 03:02
28 Jul 2021, 03:02
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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
(A) 3
(B) 5
(C) 6
(D) 12
(E) 36
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Re: In a certain clothing store, the most expensive pair of socks sells fo
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28 Jul 2021, 21:50
28 Jul 2021, 21:50
GeminiHeat 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
(A) 3
(B) 5
(C) 6
(D) 12
(E) 36
Let the price of expensive pair be \(e\) and that of cheapest pair be \(c\)
\(e = 2c - 1\)
Let \(n\) be the number of cheaper pair purchased. So,
\(18 = nc - 3e\)
\(18 = nc - 3(2c - 1)\)
\(18 = nc - 6c + 3\)
\(15 = (n - 6)c\)
\(c = \frac{15}{(n - 6)}\)
Now, for \(c\) to be an integer \(n > 6\), eliminate A, B and C
Also, for \(n = 36\), \(c = 0.5\) which is not possible
Hence, option D
gmatclubot
Re: In a certain clothing store, the most expensive pair of socks sells fo [#permalink]
28 Jul 2021, 21:50
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