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kakz: Senior | Next Rank: 100 Posts; Posts: 32; Joined: Tue Sep 13, 2011 1:02 am; Thanked: 2 times

by kakz » Sun Feb 19, 2012 12:02 pm

In a certain club that has 100 members, more number of members speak Spanish than French. If 70 members speak French and 25 speak neither Spanish nor French, what is the minimum number of members who speak both Spanish and French?

Answer is 66

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Source: Beat The GMAT — Problem Solving | Sun Feb 19, 2012 12:02 pm

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Mike@Magoosh: GMAT Instructor; Posts: 768; Joined: Wed Dec 28, 2011 4:18 pmFollowed by: 140 members; Location: Berkeley, CA; Thanked: 387 times

by Mike@Magoosh » Sun Feb 19, 2012 5:38 pm

Hi, there. I'm happy to help with this.

I never know how to make a double matrix solution look neat in the plaintext format of these posts, so I prepared a full solution in the pdf attached.

The double matrix method is a powerful method for solving problems like this. In Magoosh, among our over 100 Math Lesson Videos, we have one that demonstrates exactly how to use the double matrix method. See https://gmat.magoosh.com/plans for details.

Here's a free question along the same lines:

https://gmat.magoosh.com/admin/questions/21

Once you enter a solution to the question at that link, it should be followed by a video that gives a complete explanation.

I hope this helps. Let me know if you have any further questions.

Mike

Attachments

Club with Spanish & French speakers.pdf: (36.04 KiB) Downloaded 136 times

Magoosh GMAT Instructor
https://gmat.magoosh.com/

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