In a neighborhood having 90 households, 11 did not have

Question

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

BDSunDevil · Answer

I think 35. see the chart.

cyberjadugar · Answer

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.

cyberjadugar · Answer

Use this Venn diagram:

Bunuel · Answer

{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.

nishantmehra01 · Answer

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.

Bunuel · Answer

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.

ParmarKarishma · Answer

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

PareshGmat · Answer

Refer diagram below

Answer = 35

PareshGmat · Answer

yes its same; Please refer the diagram in above post

11 don't have car & bikes (They are out of the vehicles set)

KrishnakumarKA1 · Answer

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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JeffTargetTestPrep · Answer

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

TheNightKing · Answer

Total = 90

None = 11

We are left with 79.

Imagine a 2D Venn diagram (if you want to):

Both = 12
Only Car = 44-12=32.
Only Bike = x

12+32+x=79. So the answer has to end in 5. Option B.

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In a neighborhood having 90 households, 11 did not have

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