Problem Solving

Hi infiniti007,

Overlapping Sets questions (such as this one) are more about organization information than anything else (the math involved is almost always basic Arithmetic). You can organize the information in a number of different ways. I prefer using the Tic-Tac-Toe board for these types of prompts. This type of approach goes by a few different names, but it's just a Tic-Tac-Toe board with numbers in it.

The numbers in black are the ones that we're given.
The numbers in red are ones that you can immediately deduce (since the Grand Total = 100%).
The numbers in blue are ones that you can calculate after the ones in red.




Final Answer: E

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

Mitch's "group grid" approach is also known as the Double Matrix Method (David calls it "Double Set Matrix, and Rich calls it a Tic-Tac-Toe board). This technique can be used for most questions featuring a population in which each member has two characteristics associated with it.
Here, we have a population of Americans , and the two characteristics are:
- owning an automobile or not owning an automobile
- owning a bicycle or not owning a bicycle

This question type is VERY COMMON on the GMAT, so be sure to master the technique.

To learn more about the Double Matrix Method, watch our free video: https://www.gmatprepnow.com/module/gmat- ... ems?id=919

Once you're familiar with this technique, you can attempt these additional practice questions:

Easy Problem Solving questions
- https://www.beatthegmat.com/the-aam-aadm ... 72242.html
- https://www.beatthegmat.com/finance-majo ... 67425.html

Medium Problem Solving questions
- https://www.beatthegmat.com/probability- ... 73360.html
- https://www.beatthegmat.com/posted-speed ... 72374.html
- https://www.beatthegmat.com/motel-t271938.html
- https://www.beatthegmat.com/of-the-appli ... 70255.html
- https://www.beatthegmat.com/opening-nigh ... 64869.html
- https://www.beatthegmat.com/ds-french-ja ... 22297.html
- https://www.beatthegmat.com/prblem-solving-t279424.html

Difficult Problem Solving questions
- https://www.beatthegmat.com/ratio-problem-t268339.html
- https://www.beatthegmat.com/overlapping- ... 65223.html
- https://www.beatthegmat.com/fractions-t264254.html
- https://www.beatthegmat.com/overlapping- ... 64092.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-2

Easy Data Sufficiency questions
- https://www.beatthegmat.com/for-what-per ... 70596.html
- https://www.beatthegmat.com/ds-quest-t187706.html

Medium Data Sufficiency questions
- https://www.beatthegmat.com/sets-matrix-ds-t271914.html
- https://www.beatthegmat.com/each-of-peop ... 71375.html
- https://www.beatthegmat.com/a-manufacturer-t270331.html
- https://www.beatthegmat.com/in-costume-f ... 69355.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-1

Difficult Data Sufficiency questions
- https://www.beatthegmat.com/double-set-m ... 71423.html
- https://www.beatthegmat.com/sets-t269449.html
- https://www.beatthegmat.com/mba/2011/05/ ... question-3

Cheers,
Brent

infiniti007 wrote:Can anyone help me understand how to use the "Double Set Matrix" or "Tic Tac Toe" method to solve the following similar problem? I think I'm running astray somewhere (see image below). If this problem doesn't lend itself to the method, is there a key way to identify why not? Thanks in advance!




In a certain state, 70% of the counties received some rain on Monday, and 65% of the counties received some rain on Tuesday. No rain fell either day in 25% of the countries in the state. What percent of the countries received some rain on Monday and Tuesday?

A) 12.5%
B) 40%
C) 50%
D) 60%
E) 67.5%

Hint:
We have a population of districts , and the two characteristics are:
- rain on Monday or no rain on Monday
- rain on Tuesday or no rain on Tuesday

So, your columns can be named rain Monday and no rain Monday
Your rows can be named rain Tuesday and no rain Tuesday

See how you do with that.

Cheers,
Brent