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A certain boat sales lot sells both sailboats and boats that

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huda
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A certain boat sales lot sells both sailboats and boats that [#permalink] New post   08 Jan 2020, 14:50
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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%
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E
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Re: A certain boat sales lot sells both sailboats and boats that [#permalink] New post   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%.
So, Answer will be E.
Hope it helps!
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Re: A certain boat sales lot sells both sailboats and boats that [#permalink] New post   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] New post   14 Jan 2020, 10:09
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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] New post   17 Oct 2021, 00:42
RSQUANT wrote:
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.


I am getting the same answer too.
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Re: A certain boat sales lot sells both sailboats and boats that [#permalink] New post   15 Dec 2022, 22:42
I also got 67% would be nice if the answer can be re-verified? Since 69% makes no sense.
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Re: A certain boat sales lot sells both sailboats and boats that [#permalink] New post   15 Dec 2022, 23:29
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Let total boats = 100
Non-sail boats = y

We know, used sailboats = 25 (from qu.) and new non-sail boats = 3y/5
So, used NON-sailboats = 2y/5
Also, total used boats = 33
so, 25 + 2y/5 = 33
Or y = 20
so new non-sail boats = 12 (3y/5)
67% of all boats are new.
So new sail boats = 67-12 = 55
Total sail boats (used + non used ) = 55+25 = 80

%age of new sail boats = 55/80 * 100 ~~ 69% E
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Re: A certain boat sales lot sells both sailboats and boats that [#permalink] New post   19 Dec 2023, 15:46
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Let total number of boats be b

So used sailboat = 0.25b

All used boats = 0.33b


New sailboat = a


Total new boat = 0.67b


used non sailboat = 0.08b

total non sailboat = y


number of nonsailboats that are new = 0.6y

Total number of sailboats = x


0.08b + 0.6y = y

0.08b= 0.4y

b=5y


Required percent

x-0.25b/x


4y-1.25y/4y

2.75y/4y x 100

68.75%

Approx 69%

Answer E

Adewale Fasipe, GRE/GMAT quant instructor from Nigeria

https://www.teacheron.com/tutor-profile/8tG7?r=8tG7
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Re: A certain boat sales lot sells both sailboats and boats that [#permalink] New post   25 Mar 2025, 03:05
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Re: A certain boat sales lot sells both sailboats and boats that [#permalink]
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