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A milliner bought a job lot of hats 1/4 of which were brown.
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Updated on: 22 Nov 2018, 09:54
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35% (medium)
Question Stats:
71% (02:06) correct 29% (02:31) wrong based on 208 sessions
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A milliner bought a job lot of hats 1/4 of which were brown. The milliner sold 2/3 of the hats including 4/5 of the brown hats. What fraction of the unsold hats were brown?
(A) 1/60 (B) 2/15 (C) 3/20 (D) 3/5 (E) 3/4
Project PS Butler : Question #34
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Concentration: General Management, Entrepreneurship
GMAT 1: 750 Q49 V44
GPA: 3.38
WE: Engineering (Computer Software)
Re: A milliner bought a job lot of hats 1/4 of which were brown.
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14 Aug 2011, 03:27
i went a more difficult way to solve it,
if x = the total number of hats, then x/4 are brown hats and 3x/4 are black hats
if you sell 2/3 of the hats, and since you don't know how many of those are black or brown luckily they give you the statement that 4/5 of the brown hats were sold off in that
so 2/3x = (x/4)*(4x/5) + Y(3x/4)
I let Y be the fraction of Black hats sold, and as you can see, I included the 3x/4 which is the amount of black hats originally.
2/3*x - 1/5*x = Y(3x/4) 7x/15 = Y(3x/4)
you end up with Y = 28/60 or 14/30, or in other words, the amount of black hats sold from the original 3/4.
but earlier we also figured out that 1/5*x is the amount of brown hats sold from the original 1/4. So i guess the tricky part is realizing you need to find out what is remaining after being sold. that would equal the original amount - the sold amount.
1/4*x - 1/5*x = the remaining brown hats = 1/20*x 3/4*x - 14/30*x = the remaining black hats = 45/60*x - 28/60*x = 17/60*x
the question asks for the ratio of remaining brown to total, so divide remaining brown / total
Re: A milliner bought a job lot of hats 1/4 of which were brown.
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21 Aug 2011, 08:51
We know 1/4 of the hats are brown acc. to given conditions 4/5th of brown hats are sold so 1/5 are unsold i.e. 1/5*(no. of brown hats are unsold) Let total no. of hats be H no.of brown hats remaining=1/4*(total no. of hats)=1/4H acc. to given conditions, 1/3 hats remain hence no. of hats remaining=1/3H there required fraction=(1/20*H)/(1/3*H)=3/20 3/20
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Re: A milliner bought a job lot of hats 1/4 of which were brown.
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09 Feb 2019, 08:05
nick_sun wrote:
A milliner bought a job lot of hats 1/4 of which were brown. The milliner sold 2/3 of the hats including 4/5 of the brown hats. What fraction of the unsold hats were brown?
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71% (02:06) correct 
