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09 Jan 2020, 04:56
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
39% (03:00) correct
61%
(03:16)
wrong
based on 127
sessions
History
Date
Time
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Not Attempted Yet
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%
(A) 31%
(B) 33%
(C) 67%
(D) 68%
(E) 69%
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.
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!
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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dips1122
Joined: 12 Oct 2019
Last visit: 24 Feb 2022
Posts: 72
Given Kudos: 92
Location: India
Concentration: Marketing, General Management
Schools: ISB'22 (A) Tuck '23 (A$) Ross '23 (WL) IIMA PGPX'22 (WA) Fuqua '23 (WL) Darden '23 (WD) Cambridge '22 (D)
GMAT 1: 720 Q48 V41
GMAT 2: 730 Q50 V39
GMAT 3: 760 Q50 V44
GPA: 4
WE:Information Technology (Computer Software)
Products:
Schools: ISB'22 (A) Tuck '23 (A$) Ross '23 (WL) IIMA PGPX'22 (WA) Fuqua '23 (WL) Darden '23 (WD) Cambridge '22 (D)
GMAT 3: 760 Q50 V44
Posts: 72
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
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
