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# At a certain dealership, every car on the lot has at least one of the

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Math Expert
Joined: 02 Sep 2009
Posts: 52906
At a certain dealership, every car on the lot has at least one of the  [#permalink]

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22 Jan 2015, 06:27
00:00

Difficulty:

45% (medium)

Question Stats:

65% (02:02) correct 35% (02:48) wrong based on 80 sessions

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At a certain dealership, every car on the lot has at least one of the three modest options: windows, brakes and radio. 40 cars have windows, 30 have brakes, and 50 have a radio. 21 cars have brakes and radio, 13 have windows and brakes. 17 have windows and radio. If 11 cars have all 3 options, what is the total number of cars on the lot ?

A. 69
B. 70
C. 80
D. 91
E. 120

Kudos for a correct solution.

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Joined: 21 Sep 2013
Posts: 27
Location: United States
Concentration: Finance, General Management
GMAT Date: 10-25-2013
GPA: 3
WE: Operations (Mutual Funds and Brokerage)
Re: At a certain dealership, every car on the lot has at least one of the  [#permalink]

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22 Jan 2015, 06:37
Bunuel wrote:
At a certain dealership, every car on the lot has at least one of the three modest options: windows, brakes and radio. 40 cars have windows, 30 have brakes, and 50 have a radio. 21 cars have brakes and radio, 13 have windows and brakes. 17 have windows and radio. If 11 cars have all 3 options, what is the total number of cars on the lot ?

A. 69
B. 70
C. 80
D. 91
E. 120

Kudos for a correct solution.

total = Windows +brakes+radio -(Brk & rad +wind & brk + wind & radio ) + all 3
=40+30+50-(21+13+17)+11
=80
Manager
Joined: 14 Jul 2014
Posts: 92
Re: At a certain dealership, every car on the lot has at least one of the  [#permalink]

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22 Jan 2015, 23:18
Yup 80

Used same Gclub formula as mentioned above
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1821
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: At a certain dealership, every car on the lot has at least one of the  [#permalink]

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23 Jan 2015, 00:49
1

Refer Venn diagram below:

Attachment:

squ.png [ 5.94 KiB | Viewed 1434 times ]

Total = 40 + 10 + 7 + 23 = 80
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Manager
Status: Gmat Prep
Joined: 22 Jul 2011
Posts: 74
Re: At a certain dealership, every car on the lot has at least one of the  [#permalink]

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23 Jan 2015, 06:40
W+R+B=
-All cars with one feature counted once
-All cars with two features counted twice
-All cars with all features counted thrice

When we correct for the twice we subtract cars with two features

As we know that two features will include cars having all features in each of the three combinations of two features cars. So we end subtracting all the cars with all features therefore we add the count of cars with three feature

So
W+R+B-W&B-W&R-R&B+W&B&R
40+50+30-13-17-21+11=80.

Posted from my mobile device
Intern
Joined: 13 Dec 2018
Posts: 7
Re: At a certain dealership, every car on the lot has at least one of the  [#permalink]

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18 Jan 2019, 05:43
Bunuel wrote:
At a certain dealership, every car on the lot has at least one of the three modest options: windows, brakes and radio. 40 cars have windows, 30 have brakes, and 50 have a radio. 21 cars have brakes and radio, 13 have windows and brakes. 17 have windows and radio. If 11 cars have all 3 options, what is the total number of cars on the lot ?

A. 69
B. 70
C. 80
D. 91
E. 120

Kudos for a correct solution.

Hi!
Do you have the official answer? Because I find 47 which is not included in answer choices. To me the correct formula is: Total= 40 + 30 + 50 - 21 - 13 - 17 - 2(11) = 47 Is that right?
Manager
Joined: 21 Jun 2017
Posts: 234
Concentration: Finance, Economics
WE: Corporate Finance (Commercial Banking)
Re: At a certain dealership, every car on the lot has at least one of the  [#permalink]

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18 Jan 2019, 06:14
1
Malbash212 wrote:
Bunuel wrote:
At a certain dealership, every car on the lot has at least one of the three modest options: windows, brakes and radio. 40 cars have windows, 30 have brakes, and 50 have a radio. 21 cars have brakes and radio, 13 have windows and brakes. 17 have windows and radio. If 11 cars have all 3 options, what is the total number of cars on the lot ?

A. 69
B. 70
C. 80
D. 91
E. 120

Kudos for a correct solution.

Hi!
Do you have the official answer? Because I find 47 which is not included in answer choices. To me the correct formula is: Total= 40 + 30 + 50 - 21 - 13 - 17 - 2(11) = 47 Is that right?

Hi the formula you are applying is when the intersections are "exactly two group overlaps" . This question includes"sum of two group overlaps".
_________________

Even if it takes me 30 attempts, I am determined enough to score 740+ in my 31st attempt. This is it, this is what I have been waiting for, now is the time to get up and fight, for my life is 100% my responsibility.

Dil ye Ziddi hai !!!

Intern
Joined: 18 Jan 2019
Posts: 8
Re: At a certain dealership, every car on the lot has at least one of the  [#permalink]

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18 Jan 2019, 07:02
Intern
Joined: 13 Dec 2018
Posts: 7
Re: At a certain dealership, every car on the lot has at least one of the  [#permalink]

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18 Jan 2019, 07:30
ShankSouljaBoi wrote:
Malbash212 wrote:
Bunuel wrote:
At a certain dealership, every car on the lot has at least one of the three modest options: windows, brakes and radio. 40 cars have windows, 30 have brakes, and 50 have a radio. 21 cars have brakes and radio, 13 have windows and brakes. 17 have windows and radio. If 11 cars have all 3 options, what is the total number of cars on the lot ?

A. 69
B. 70
C. 80
D. 91
E. 120

Kudos for a correct solution.

Hi!
Do you have the official answer? Because I find 47 which is not included in answer choices. To me the correct formula is: Total= 40 + 30 + 50 - 21 - 13 - 17 - 2(11) = 47 Is that right?

Hi the formula you are applying is when the intersections are "exactly two group overlaps" . This question includes"sum of two group overlaps".

Thank you for your answer. Is it different from this one: https://gmatclub.com/forum/there-are-70 ... 97623.html
Manager
Joined: 21 Jun 2017
Posts: 234
Concentration: Finance, Economics
WE: Corporate Finance (Commercial Banking)
Re: At a certain dealership, every car on the lot has at least one of the  [#permalink]

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18 Jan 2019, 07:37
Malbash212

Yes ! You got that right. Learn this formula, under exam conditions you will not get it right. Trust me on that. best of luck
_________________

Even if it takes me 30 attempts, I am determined enough to score 740+ in my 31st attempt. This is it, this is what I have been waiting for, now is the time to get up and fight, for my life is 100% my responsibility.

Dil ye Ziddi hai !!!

Re: At a certain dealership, every car on the lot has at least one of the   [#permalink] 18 Jan 2019, 07:37
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