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In a neighborhood having 90 households, 11 did not have

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In a neighborhood having 90 households, 11 did not have [#permalink] New post 23 May 2012, 11:24
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94% (02:27) correct 6% (01:59) wrong based on 65 sessions
In a neighborhood having 90 households, 11 did not have either a car or a bike. If 12 households had a both a car and a bike and 44 had a car, how many had bike only?

A. 30
B. 35
C. 20
D. 18
E. 10
[Reveal] Spoiler: OA
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Re: Sets - Neighbourhood bikes [#permalink] New post 23 May 2012, 11:42
I think 35. see the chart.
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Re: Sets - Neighbourhood bikes [#permalink] New post 23 May 2012, 23:33
Hi,

Total households = 90
Households having car or bike = 90-11 = 79
Households having car = 44
Households having bike only = 79 - 44 = 35

(B)

Redundant information: 12 households had a both a car and a bike.
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Re: In a neighborhood having 90 households, 11 did not have [#permalink] New post 23 May 2012, 23:36
Use this Venn diagram:
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Re: In a neighborhood having 90 households, 11 did not have [#permalink] New post 23 May 2012, 23:40
Expert's post
navigator123 wrote:
In a neighborhood having 90 households, 11 did not have either a car or a bike. If 12 households had a both a car and a bike and 44 had a car, how many had bike only?

A. 30
B. 35
C. 20
D. 18
E. 10


{Total}={Car}+{Bike}-{Both}+{Neither} --> 90=44+{Bike}-12+11 --> {Bike}=47 --> # those who have bike only is {Bike}-{Both}=47-12=35.

Answer: B.

Hope it's clear.
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Re: In a neighborhood having 90 households, 11 did not have [#permalink] New post 20 Jun 2012, 22:55
N(Car or Bike) = N(Car) + N(Bike) - N(Car + Bike)

N(Car or Bike) = 90-11 = 79

N(Car) = 44

N(Car + Bike) = 12

79 = 44 + N(Bike) - 12

N (Bike) = 47

But this includes people with Bike and Car both.

People with just Bike = 47 - 12 = 35

Pls tell where I am wrong.

navigator123 wrote:
In a neighborhood having 90 households, 11 did not have either a car or a bike. If 12 households had a both a car and a bike and 44 had a car, how many had bike only?

A. 30
B. 35
C. 20
D. 18
E. 10
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Re: In a neighborhood having 90 households, 11 did not have [#permalink] New post 21 Jun 2012, 00:46
Expert's post
nishantmehra01 wrote:
N(Car or Bike) = N(Car) + N(Bike) - N(Car + Bike)

N(Car or Bike) = 90-11 = 79

N(Car) = 44

N(Car + Bike) = 12

79 = 44 + N(Bike) - 12

N (Bike) = 47

But this includes people with Bike and Car both.

People with just Bike = 47 - 12 = 35

Pls tell where I am wrong.

navigator123 wrote:
In a neighborhood having 90 households, 11 did not have either a car or a bike. If 12 households had a both a car and a bike and 44 had a car, how many had bike only?

A. 30
B. 35
C. 20
D. 18
E. 10


You did nothing wrong: answer B is correct. Though after you got that N(Car or Bike) = 79 and N(Car) = 44, you could directly subtract from the group who has a car or a bike (79) the group who has a car (44) to get the group who has only bike: 79-44=35.

Hope it's clear.
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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: In a neighborhood having 90 households, 11 did not have [#permalink] New post 15 Aug 2013, 10:02
Bunuel wrote:
navigator123 wrote:
In a neighborhood having 90 households, 11 did not have either a car or a bike. If 12 households had a both a car and a bike and 44 had a car, how many had bike only?

A. 30
B. 35
C. 20
D. 18
E. 10


{Total}={Car}+{Bike}-{Both}+{Neither} --> 90=44+{Bike}-12+11 --> {Bike}=47 --> # those who have bike only is {Bike}-{Both}=47-12=35.

Answer: B.

Hope it's clear.



Is "11 did not have either a car or a bike" same as "11 did have neither a car nor a bike" ?
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Re: In a neighborhood having 90 households, 11 did not have [#permalink] New post 06 Sep 2014, 21:42
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Re: In a neighborhood having 90 households, 11 did not have [#permalink] New post 08 Sep 2014, 00:16
Refer diagram below

Answer = 35
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In a neighborhood having 90 households, 11 did not have [#permalink] New post 08 Sep 2014, 00:20
ParmarKarishma wrote:
Bunuel wrote:
navigator123 wrote:
In a neighborhood having 90 households, 11 did not have either a car or a bike. If 12 households had a both a car and a bike and 44 had a car, how many had bike only?

A. 30
B. 35
C. 20
D. 18
E. 10


{Total}={Car}+{Bike}-{Both}+{Neither} --> 90=44+{Bike}-12+11 --> {Bike}=47 --> # those who have bike only is {Bike}-{Both}=47-12=35.

Answer: B.

Hope it's clear.



Is "11 did not have either a car or a bike" same as "11 did have neither a car nor a bike" ?


yes its same; Please refer the diagram in above post

11 don't have car & bikes (They are out of the vehicles set)
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In a neighborhood having 90 households, 11 did not have   [#permalink] 08 Sep 2014, 00:20
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