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# A certain boat sales lot sells both sailboats and boats that

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A certain boat sales lot sells both sailboats and boats that [#permalink]  08 Jan 2020, 14:50
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Question Stats:

29% (02:42) correct 70% (02:20) wrong based on 34 sessions
A certain boat sales lot sells both sailboats and boats that are not sailboats. 25% of the boats are used sailboats. Of non-sailboats, $$\frac{3}{5}$$ are new. If 33% of all boats are used, approximately what percentage of the sailboats are new?

(A) 31%
(B) 33%
(C) 67%
(D) 68%
(E) 69%
[Reveal] Spoiler: OA

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Re: A certain boat sales lot sells both sailboats and boats that [#permalink]  11 Jan 2020, 10:11
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This question can be solved using overlapping sets 2x2 matrix. PFA The first image which talks about the things which are given in the question.
Now we are asked to find what percentage of the sailboats are new, which is nothing but $$\frac{Sailboats Which Are New }{ Total Sailboats}*100%$$
Now, see the second image attached. Let's calculate Used Non Sailboats. Using the Used column we will get number of used non-sailboats as 33-25 = 8
Using the Non-sailboat row we will get number of used non-sailboats as x = 3x/5 = 2x/5
=> 2x/5 = 8 => x = 20
So, Total Sailboats = 100-x = 100-20 = 80
New Sailboats = Total Sailboats - Used = 80 - 25 = 55
So, percentage of the sailboats are new = $$\frac{Sailboats Which Are New }{ Total Sailboats}$$ = $$\frac{55 }{ 80}* 100%$$ = 68.75% ~ 69%.
Hope it helps!
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Re: A certain boat sales lot sells both sailboats and boats that [#permalink]  14 Jan 2020, 03:00
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huda wrote:
A certain boat sales lot sells both sailboats and boats that are not sailboats. 25% of the boats are used sailboats. Of non-sailboats, $$\frac{3}{5}$$ are new. If 33% of all boats are used, approximately what percentage of the sailboats are new?

(A) 31%
(B) 33%
(C) 67%
(D) 68%
(E) 69%

Sorry to reply the answer in the form of an image but have to as it's a Venn diagram question. Please could the author check the answer as my answer is 67%. The 3/5th of Non sail boats information is not required.
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Re: A certain boat sales lot sells both sailboats and boats that [#permalink]  14 Jan 2020, 10:09
Expert's post
Great guys for the explanations.

Thank you so much.

Regards
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Re: A certain boat sales lot sells both sailboats and boats that   [#permalink] 14 Jan 2020, 10:09
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