NEW HERE? LEARN MORE
closeclose
Last visit was: 29 Apr 2024, 03:07 It is currently 29 Apr 2024, 03:07
Decision Tracker
My Rewards
New posts
New comers' posts

Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

An auto manufacturer produces two body styles, sedan and convertible,

User avatar
L
Sajjad1994
GRE Forum Moderator
Joined: 02 Nov 2016
Posts: 13966
Own Kudos [?]: 33023 [12]
Given Kudos: 5781
GPA: 3.62
Send PM
CAT Tests Forum Quiz Mode
An auto manufacturer produces two body styles, sedan and convertible, [#permalink] New post   17 Oct 2023, 05:05
12
Bookmarks
Expert Reply
00:00

Difficulty:

95% (hard)

Question Stats:

26% (03:24) correct 74% (03:33) wrong based on 155 sessions
Hide Show timer Statistics
Data Insights (DI) Butler 2023-24 [Question #47, Date: Oct-17-2023]


An auto manufacturer produces two body styles, sedan and convertible, each available in black, white, silver, red, and blue. Upholstery and interiors can be ordered in black, white, red, or blue, but the manufacturer will not put a red interior in a blue body or a blue interior in a red body. For an auto show, the manufacturer wants to display different available combinations to the limit of the space available. Because silver is considered too common, the decision is made not to display any vehicles with silver bodies. The number of remaining combinations is too large for the available space, so the decision is made to display half the interior/exterior color combinations as sedans and half as convertibles. Find the number of vehicle combinations that are actually possible and the number of vehicles that will be displayed.
Number of possible combinations Number of vehicles to be displayed
14
18
24
28
34
36
Submit
Click Submit to add this question to your Error log
ShowHide Answer
Official Answer
Number of possible combinations: 36
Number of vehicles to be displayed: 14
User avatar
B
kryinkrumble
Intern
Intern
Joined: 14 Oct 2023
Posts: 32
Own Kudos [?]: 25 [0]
Given Kudos: 54
Location: Singapore
Schools: Imperial (A) LBS (A)
GMAT Focus 1:
675 Q88 V83 DI80
Send PM
Re: An auto manufacturer produces two body styles, sedan and convertible, [#permalink] New post   Updated on: 18 Oct 2023, 02:45
Number of possible combinations = 2*[(4*4)-2] =28 -> There are 4 possible types of exterior colours (excluding silver) and 4 possible types of interior colours and we have to exclude red exterior blue interior and red interior blue exterior. In addition, we have to consider that all these combination can apply for both sedans and convertible.

Number of cars on display = 28/2 = 14 -> decision is to display half the combinations for convertible and sedan respectively.

Originally posted by kryinkrumble on 17 Oct 2023, 23:42.
Last edited by kryinkrumble on 18 Oct 2023, 02:45, edited 2 times in total.
User avatar
S
mendax
Manager
Manager
Joined: 23 Aug 2021
Posts: 89
Own Kudos [?]: 65 [2]
Given Kudos: 14
WE:Design (Energy and Utilities)
Send PM
GMAT ToolKit User Forum Quiz Mode
Re: An auto manufacturer produces two body styles, sedan and convertible, [#permalink] New post   18 Oct 2023, 02:42
2
Kudos
Excluding Silver, there will be 4 types of exterior colors that are Black, Blue, White and Red and 4 same interior colors. The pairs which is excluded in exterior/interior combinations are Red/Blue or Blue/Red.

For each of the Black and White exterior => 4 possible interior colors are available
For each of the Blue and Red exteriror => 3 possible interior colors are available
Total possible combinations for each type of car => 4+4+3+3=> 14
So total combination of sedan and convertible => 28
Since half of the 14 combinations will be used in convertible and half in sedan, total vehicles to be displayed in auto show => 14
User avatar
G
pudu
Senior Manager
Senior Manager
Joined: 12 Mar 2023
Posts: 293
Own Kudos [?]: 94 [0]
Given Kudos: 16
Location: India
Send PM
Re: An auto manufacturer produces two body styles, sedan and convertible, [#permalink] New post   20 Oct 2023, 02:47
how it is 38? is it correct?
User avatar
G
pudu
Senior Manager
Senior Manager
Joined: 12 Mar 2023
Posts: 293
Own Kudos [?]: 94 [0]
Given Kudos: 16
Location: India
Send PM
Re: An auto manufacturer produces two body styles, sedan and convertible, [#permalink] New post   20 Oct 2023, 02:56
pudu wrote:
how it is 38? is it correct?



please explain how to get total of 38 combinations?
User avatar
L
Sajjad1994
GRE Forum Moderator
Joined: 02 Nov 2016
Posts: 13966
Own Kudos [?]: 33023 [0]
Given Kudos: 5781
GPA: 3.62
Send PM
CAT Tests Forum Quiz Mode
Re: An auto manufacturer produces two body styles, sedan and convertible, [#permalink] New post   20 Oct 2023, 08:02
Expert Reply
Official Explanation

At first glance, there are 40 possible models: 2 body types × 5 exterior colors × 4 interior colors. However, you also must subtract the four combinations the company refuses to make: the blue with red interior and the red with blue interior for both sedan and convertibles. Therefore, there are 36 possible combinations. When the decision is made not to show the silver, the number is reduced to 2 × 4 × 4 – 2 = 30 cars, but that is too many for the space. Therefore, the 4 × 4 – 2 = 14 interior/exterior color combinations will be displayed as 7 sedans and 7 convertibles.
User avatar
G
pudu
Senior Manager
Senior Manager
Joined: 12 Mar 2023
Posts: 293
Own Kudos [?]: 94 [2]
Given Kudos: 16
Location: India
Send PM
Re: An auto manufacturer produces two body styles, sedan and convertible, [#permalink] New post   20 Oct 2023, 08:52
2
Kudos
Sajjad1994 wrote:
Official Explanation

At first glance, there are 40 possible models: 2 body types × 5 exterior colors × 4 interior colors. However, you also must subtract the two combinations the company refuses to make: the blue with red interior and the red with blue interior. Therefore, there are 38 possible combinations. When the decision is made not to show the silver, the number is reduced to 2 × 4 × 4 – 2 = 30 cars, but that is too many for the space. Therefore, the 4 × 4 – 2 = 14 interior/exterior color combinations will be displayed as 7 sedans and 7 convertibles.


yes up to 40 was rght...then what i did is instead of subtracting 2 i subtract 4 and got 36....thank you so much
User avatar
B
MHBS
Manager
Manager
Joined: 22 Mar 2023
Posts: 56
Own Kudos [?]: 8 [2]
Given Kudos: 14
Location: India
Concentration: Finance, General Management
WE:Engineering (Energy and Utilities)
Send PM
Re: An auto manufacturer produces two body styles, sedan and convertible, [#permalink] New post   21 Oct 2023, 02:46
2
Kudos
Sajjad1994 wrote:
Official Explanation

At first glance, there are 40 possible models: 2 body types × 5 exterior colors × 4 interior colors. However, you also must subtract the two combinations the company refuses to make: the blue with red interior and the red with blue interior. Therefore, there are 38 possible combinations. When the decision is made not to show the silver, the number is reduced to 2 × 4 × 4 – 2 = 30 cars, but that is too many for the space. Therefore, the 4 × 4 – 2 = 14 interior/exterior color combinations will be displayed as 7 sedans and 7 convertibles.


Sajjad1994
In that case , the no of combinations with the blue with red interior and the red with blue interior are 4 . Two for Sedan & 2 for convertible. Then it is 40-4 = 36
User avatar
B
Starscreen60
Intern
Intern
Joined: 02 Mar 2023
Posts: 24
Own Kudos [?]: 9 [0]
Given Kudos: 15
Location: India
Schools: IESE '26 (A) HEC Sep'24 Intake (A)
GMAT Focus 1:
645 Q80 V83 DI82
GPA: 2.96
Send PM
Re: An auto manufacturer produces two body styles, sedan and convertible, [#permalink] New post   20 Nov 2023, 02:59
Sajjad1994 38 is wrong. When you have 5x4 combinations in total, that's 40 options. The manufacturer won't combine red paint and blue interior for both Sedan AND Convertibles. That's 4 options out:
- Sedan: Red with blue interior, Blue with red interior
- Convertible: Red with blue interior, Blue with red interior
User avatar
L
Sajjad1994
GRE Forum Moderator
Joined: 02 Nov 2016
Posts: 13966
Own Kudos [?]: 33023 [0]
Given Kudos: 5781
GPA: 3.62
Send PM
CAT Tests Forum Quiz Mode
Re: An auto manufacturer produces two body styles, sedan and convertible, [#permalink] New post   20 Nov 2023, 09:40
Expert Reply
Starscreen60 wrote:
Sajjad1994 38 is wrong. When you have 5x4 combinations in total, that's 40 options. The manufacturer won't combine red paint and blue interior for both Sedan AND Convertibles. That's 4 options out:
- Sedan: Red with blue interior, Blue with red interior
- Convertible: Red with blue interior, Blue with red interior


To avoid ambiguity, the question is modified.
GMAT Club Bot
gmatclubot
Re: An auto manufacturer produces two body styles, sedan and convertible, [#permalink]
20 Nov 2023, 09:40
Moderators:
Sajjad1994
GRE Forum Moderator
13966 posts
BottomJee
DI Forum Moderator
1030 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions