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swerve: Legendary Member; Posts: 2499; Joined: Sun Oct 29, 2017 2:04 pm; Followed by:6 members

Of the 500 consumers surveyed, 78 percent said they own...

by swerve » Tue Feb 27, 2018 8:12 am

Of the 500 consumers surveyed, 78 percent said they own a toaster, 65 percent said they own a microwave oven and, 52 percent said they own both a toaster and a microwave oven. How many of the consumers surveyed said that do not own either a toaster or a microwave oven?

A. 45
B. 55
C. 65
D. 95
E. 130

The OA is A.

Please, can any expert explain this PS question for me? I can't get the correct answer. I need your help. Thanks.

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Source: Beat The GMAT — Problem Solving | Tue Feb 27, 2018 8:12 am

GMAT/MBA Expert

[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pm; Location: Palo Alto, CA; Thanked: 2867 times; Followed by:511 members; GMAT Score:800

by [email protected] » Tue Feb 27, 2018 5:19 pm

Hi swerve,

We're told that of the 500 consumers surveyed, 78 percent said they own a toaster, 65 percent said they own a microwave oven and 52 percent said they own BOTH a toaster and a microwave oven. We're asked for the number of consumers surveyed who said that do not own either a toaster or a microwave oven. This question is an example of a standard Overlapping Sets question, so we can use the Overlapping Sets formula to solve it:

Total = (Group 1) + (Group 2) - Both + Neither

In this prompt, the total is 100%, 'Group 1' are those who own a toaster, 'Group 2' are those who own a microwave...

100% = 78% + 65% - 52% + (Neither)
100% = 91% + (Neither)
9% = Neither

Since there were 500 people surveyed, the number who have neither a toaster nor a microwave is 9% of 500 = (.09)(500) = 45

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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GMAT/MBA Expert

Scott@TargetTestPrep: GMAT Instructor; Posts: 8083; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Thu Mar 01, 2018 5:39 pm

swerve wrote:Of the 500 consumers surveyed, 78 percent said they own a toaster, 65 percent said they own a microwave oven and, 52 percent said they own both a toaster and a microwave oven. How many of the consumers surveyed said that do not own either a toaster or a microwave oven?

A. 45
B. 55
C. 65
D. 95
E. 130

We can use the equation:

Total = own a toaster + own a microwave - own both + own neither

However, to start we can just use percents:

100 = 78 + 65 - 52 + N

100 = 91 + N

9 = N

So 9% of 500 people or 500 x 0.09 = 45 people own neither a toaster nor a microwave.

Answer: A

Scott Woodbury-Stewart
Founder and CEO
[email protected]