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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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23 May 2012, 11:24
1
3
00:00

Difficulty:

5% (low)

Question Stats:

92% (01:51) correct 8% (02:11) wrong based on 174 sessions

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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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23 May 2012, 11:42
I think 35. see the chart.
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bike2.jpg [ 8.64 KiB | Viewed 3819 times ]

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Re: Sets - Neighbourhood bikes  [#permalink]

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23 May 2012, 23:33
1
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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23 May 2012, 23:36
Use this Venn diagram:
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Venn_d.jpg [ 15.48 KiB | Viewed 3799 times ]

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

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23 May 2012, 23:40
1
1
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.

Hope it's clear.
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Re: In a neighborhood having 90 households, 11 did not have  [#permalink]

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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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Posts: 52390
Re: In a neighborhood having 90 households, 11 did not have  [#permalink]

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21 Jun 2012, 00:46
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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Re: In a neighborhood having 90 households, 11 did not have  [#permalink]

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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.

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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08 Sep 2014, 00:16
Refer diagram below

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Vennd_d.png [ 31.52 KiB | Viewed 1874 times ]

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

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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.

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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09 Mar 2017, 01:53
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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15 Mar 2017, 15:21
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.

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