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hudacse6
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A certain boat sales lot sells both sailboats and boats that are not 09 Jan 2020, 04:56
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E
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95% (hard)

Question Stats:

40% (02:57) correct 60% (03:16) wrong based on 128 sessions

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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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BrushMyQuant
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A certain boat sales lot sells both sailboats and boats that are not Updated on: 15 Jul 2020, 10:45
Originally posted by BrushMyQuant on 09 Jan 2020, 10:37.
Last edited by BrushMyQuant on 15 Jul 2020, 10:45, edited 1 time in total.
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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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A certain boat sales lot sells both sailboats and boats that are not 10 Jan 2020, 21:29
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Tricky question.
Here's my solution:

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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A certain boat sales lot sells both sailboats and boats that are not 24 Nov 2025, 08:00
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hudacse6

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?

SailboatsNot sailboatsTotal
New67%-12% = 55%3x/5 = 12%67%
Used25%33%-25%=8%=2x/533%
Total80%x = 20%100%

2x/5=8%
x = 20%

The percentage of sailboats that are new = 55%/80% *100% = 1100/16 % = 68.75% ~ 69%

IMO E
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A certain boat sales lot sells both sailboats and boats that are not 05 Dec 2025, 07:04
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Lets take....all boat = 100 ....so 25% of all boats are used sailboats.....so...used sailboats = 25 ...... And....33% of all boats are used.....so....used boats = 33% of 100 = 33 ...... Now lets fill up the chart with what we already have....

.................................used................new..............total........

Sailboat.....................25....................??.................??..........

Non sailboat.............??....................??.................??...........

Total..........................33....................??.................100...........

So...used non sailboats are = total used boats - used sailboats = 33 - 25 = 8 .....
....and.....3 / 5 of non sailboats are new.....so....used non sailboats = 2 / 5 of all non sailboats = 8 .....
So..... [ 2 / 5 ] × [ all non sailboats ] = 8
So...... [ all non sailboats ] = 8 × [ 5 / 2 ] = 20 ...... So lets fill up the chart again......

.................................used................new..............total........

Sailboat.....................25....................??.................??..........

Non sailboat..............8....................??.................20...........

Total..........................33....................??.................100...........

So....all sailboats = 100 - 20 = 80 ..... And......new sailboats = 80 - 25 = 55

.................................used................new..............total........

Sailboat.....................25....................55.................80..........

Non sailboat.............8....................??.................20...........

Total..........................33....................??.................100...........

Now.....all sailboats = 80 .... New sailboats = 55 .....
So......da percentage of sailboats that are new = [ 55 × 100 ] / [ 80 ] = 68.75 ≈ 69

!nah id win!
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