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BTGmoderatorRO: Moderator; Posts: 772; Joined: Wed Aug 30, 2017 6:29 pm; Followed by:6 members

Word Problems

by BTGmoderatorRO » Sun Dec 17, 2017 6:20 am

In a town of 10 million households there are 3 newspapers in circulation - X, Y and Z. There are 9 million households that subscribe to one or more newspapers.The number of total circulation of all the newspapers is 12 million. The number of households subscribing to X,Y are 2 million and 5 million respectively. What is the number of households subscribing to more than 1 newspaper.Assume that any household subscribes only one newspaper of a particular type.

a. At least 3 million

b. Exactly 3 million

c. Less than 3 million

d. At least 2 million

e. At least 1.5 million

OA is E
With the aid of an Expert i would love a breakdown of this question.Thanks

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Source: Beat The GMAT — Problem Solving | Sun Dec 17, 2017 6:20 am

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by Scott@TargetTestPrep » Sat Sep 21, 2019 11:22 am

BTGmoderatorRO wrote:In a town of 10 million households there are 3 newspapers in circulation - X, Y and Z. There are 9 million households that subscribe to one or more newspapers.The number of total circulation of all the newspapers is 12 million. The number of households subscribing to X,Y are 2 million and 5 million respectively. What is the number of households subscribing to more than 1 newspaper.Assume that any household subscribes only one newspaper of a particular type.

a. At least 3 million

b. Exactly 3 million

c. Less than 3 million

d. At least 2 million

e. At least 1.5 million

OA is E
With the aid of an Expert i would love a breakdown of this question.Thanks

We will use the formula:

# of households = total circulation - # of households that subscribe to exactly 2 newspapers - 2 * # of households that subscribe to all 3 newspapers

In one extreme case, suppose that no household subscribes to all three newspapers; therefore the number of households that subscribe to more than one newspaper is the number of households that subscribe to exactly 2 newspapers. In this case, we get the maximum number of households that subscribe to more than one newspaper; which is

9 = 12 - #exactly two - 2 * 0

#exactly two = 12 - 9 = 3

In another extreme case, suppose that no household subscribes to exactly two newspapers; therefore the number of households that subscribe to more than one newspaper is the number of households that subscribe to all three newspapers. In this case, we get the minimum number of households that subscribe to more than one newspaper; which is:

9 = 12 - 0 - 2 * #all three

2 * #all three = 12 - 9 = 3

#all three = 3/2 = 1.5

Since the number of households that subscribe to more than one newspaper is between 1.5 million and 3 million, inclusive, the answer is E.

Answer: E

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