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A souvenir stand began the day Wednesday with a ratio of 13 hats for

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A souvenir stand began the day Wednesday with a ratio of 13 hats for [#permalink] New post 22 Oct 2014, 02:15
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A souvenir stand began the day Wednesday with a ratio of 13 hats for every 7 shirts. If the stand received no new hats or shirts during the day Wednesday, and the only items that left the stand were those that were sold, did the stand end the day Wednesday with more shirts than hats?

(1) During the day Wednesday, the stand sold a total of 10 hats.

(2) The stand began the day Wednesday with an even number of hats.
[Reveal] Spoiler: OA

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Last edited by Bunuel on 22 Oct 2014, 03:00, edited 1 time in total.
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A souvenir stand began the day Wednesday with a ratio of 13 hats for [#permalink] New post 22 Oct 2014, 03:11
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A souvenir stand began the day Wednesday with a ratio of 13 hats for every 7 shirts. If the stand received no new hats or shirts during the day Wednesday, and the only items that left the stand were those that were sold, did the stand end the day Wednesday with more shirts than hats?

Given that Hats:Shirts = 13x:7x.

(1) During the day Wednesday, the stand sold a total of 10 hats. If there were 13 hats and 7 shirts and no shirt was sold, then by the end of the day there would be 3 hats and 7 shirts left (S > H) but if for the same case all shirts were sold, then by the end of the day there would be 3 hats and 0 shirts left (S < H). Not sufficient.

(2) The stand began the day Wednesday with an even number of hats. This implies that x is even, so Hats:Shirts = 13x:7x = 26:14 = 52:28 = 78:42... We don't know how many of the items were sold. Not sufficient.

(1)+(2) From (2) we know that the least difference between the number of hats and shirts could be is 12 (if there were 26 hats and 14 shirts). (1) says that only 10 hats were sold, so even if 0 shirts were sold, the number of hats must be at least 2 more than the number of shirts. Thus the answer to the question is NO Sufficient.

Answer: C.

Hope it's clear.
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A souvenir stand began the day Wednesday with a ratio of 13 hats for   [#permalink] 22 Oct 2014, 03:11
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A souvenir stand began the day Wednesday with a ratio of 13 hats for

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