In a neighborhood having 90 households, 11 did not have

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BTGmoderatorLU: Moderator; Posts: 2505; Joined: Sun Oct 15, 2017 1:50 pm; Followed by:6 members

In a neighborhood having 90 households, 11 did not have

by BTGmoderatorLU » Thu Apr 05, 2018 5:27 pm

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

The OA is B.

Can anyone give me a suggestion about how can I solve this PS question? Thanks in advance.

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Source: Beat The GMAT — Problem Solving | Thu Apr 05, 2018 5:27 pm

GMATinsight: Legendary Member; Posts: 1100; Joined: Sat May 10, 2014 11:34 pm; Location: New Delhi, India; Thanked: 205 times; Followed by:24 members

by GMATinsight » Thu Apr 05, 2018 11:23 pm

BTGmoderatorLU 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

The OA is B.

Can anyone give me a suggestion about how can I solve this PS question? Thanks in advance.

Only Car + Only Bike + Car and Bike both + None = 90

None = 11
Car and Bike both = 12
Only Car+Car and Bike both = 44
i.e. Only Car = 44-12 = 32

32 + only Bike + 12 + 11 = 90

Only Bike = 35

Answer: option B

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Jay@ManhattanReview: GMAT Instructor; Posts: 3008; Joined: Mon Aug 22, 2016 6:19 am; Location: Grand Central / New York; Thanked: 470 times; Followed by:34 members

by Jay@ManhattanReview » Thu Apr 05, 2018 11:32 pm

BTGmoderatorLU 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

The OA is B.

Can anyone give me a suggestion about how can I solve this PS question? Thanks in advance.

The number of households that have either a car, a bike or both = 90 - 11 = 79
The number of households that have a car = 44 (this includes those who have both a car and a bike)

The number of households that have ONLY bike = 79 - 44 = 35.

The data '12 households had a both, a car and a bike' is redundant.

The correct answer: B

Hope this helps!

-Jay
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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Thu May 23, 2019 4:14 pm

BTGmoderatorLU 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

The OA is B.

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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