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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]

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New post 23 May 2012, 12:24
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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: Sets - Neighbourhood bikes [#permalink]

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New post 23 May 2012, 12:42
I think 35. see the chart.
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Re: Sets - Neighbourhood bikes [#permalink]

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New post 24 May 2012, 00:33
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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]

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New post 24 May 2012, 00:36
Use this Venn diagram:
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Re: In a neighborhood having 90 households, 11 did not have [#permalink]

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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]

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New post 20 Jun 2012, 23:55
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]

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New post 21 Jun 2012, 01:46
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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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]

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New post 15 Aug 2013, 11:02
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]

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New post 06 Sep 2014, 22:42
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Re: In a neighborhood having 90 households, 11 did not have [#permalink]

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New post 08 Sep 2014, 01:16
Refer diagram below

Answer = 35
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In a neighborhood having 90 households, 11 did not have [#permalink]

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New post 08 Sep 2014, 01:20
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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Re: In a neighborhood having 90 households, 11 did not have [#permalink]

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New post 05 Dec 2015, 03:36
Hello from the GMAT Club BumpBot!

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Re: In a neighborhood having 90 households, 11 did not have [#permalink]

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New post 08 Mar 2017, 21:39
Hello from the GMAT Club BumpBot!

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Re: In a neighborhood having 90 households, 11 did not have [#permalink]

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New post 09 Mar 2017, 02:53
Household (car) = household (car only) + household (both car and bike) = 44
Total household = Household(neither car nor bike) + household (car only) + household (bike only) + household (both car and bike)
or
90 = 11 +household (bike only) + 44
or household (bike only) = 90-55 =35.

Option B

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Re: In a neighborhood having 90 households, 11 did not have [#permalink]

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New post 15 Mar 2017, 16:21
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


We can use the following formula:

# of households = # with a car + # with a bike - # with both + # with neither

90 = 44 + b - 12 + 11

90 = 43 + b

47 = b

We see that 47 households had a bike and 12 of them also had a car; thus, 47 - 12 = 35 households had a bike only.

Answer: B
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Re: In a neighborhood having 90 households, 11 did not have   [#permalink] 15 Mar 2017, 16:21
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