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## In a particular state, 70 percent of the counties received..

tagged by: BTGmoderatorLU

This topic has 3 expert replies and 0 member replies

### Top Member

BTGmoderatorLU Moderator
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#### In a particular state, 70 percent of the counties received..

Thu Feb 08, 2018 6:38 am
In a particular state, 70 percent of the counties received some rain on Monday, and 65 percent of the counties received some rain on Tuesday. No rain fell either day in 25 percent of the counties in the state. What percent of the counties received some rain on Monday and Tuesday?

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

The OA is D.

I'm confused by this PS question. Experts, any suggestion? Thanks in advance.

### GMAT/MBA Expert

ErikaPrepScholar Legendary Member
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Thu Feb 08, 2018 8:08 am
We can solve this problem by filling in the information we know using a double matrix.
[img]https://cl.ly/3q3U1q2s3R1E[/img]

Filling in only the information in the question gives us:
[img]https://cl.ly/162J2X0m1u2c[/img]

We want to know the number of counties that received some rain on both Monday and Tuesday. In other words, we want to find the value in the top left cell (Monday rain + Tuesday rain).

Next, in any row that has two filled-in cells, we can use that information to fill in the third cell in the row:
[img]https://cl.ly/2j420X0a023K[/img]

Then again:
[img]https://cl.ly/1x272X0e2e2L[/img]

Then again:
[img]https://cl.ly/3K1U1k3T3T3V[/img]

So 60% of the counties received some rain on both Monday and Tuesday.

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### GMAT/MBA Expert

Rich.C@EMPOWERgmat.com Elite Legendary Member
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Thu Feb 08, 2018 10:22 am
Hi LUANDATO,

We're told that in a particular state, 70 percent of the counties received some rain on Monday, 65 percent of the counties received some rain on Tuesday and no rain fell either day in 25 percent of the counties in the state. We're asked for the percent of the counties that received some rain on Monday AND Tuesday. This prompt is an example of a standard 'Overlapping Sets' question and we can use the Overlapping Sets Formula to answer it.

The Overlapping Sets Formula is...
Total = (Group 1) + (Group 2) - (Both) + (Neither)

In this prompt, Group 1 is the "Monday rain" group and Group 2 is the "Tuesday rain" group:
Total = (Group 1) + (Group 2) - (Both) + (Neither)
100% = (70%) + (65%) - (Both) + (25%)
100% = 160% - (Both)
Both = 60%

Thus, 60% of the counties received rain on BOTH days.

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

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Contact Rich at Rich.C@empowergmat.com

### GMAT/MBA Expert

Jeff@TargetTestPrep GMAT Instructor
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Mon Feb 12, 2018 4:50 pm
LUANDATO wrote:
In a particular state, 70 percent of the counties received some rain on Monday, and 65 percent of the counties received some rain on Tuesday. No rain fell either day in 25 percent of the counties in the state. What percent of the counties received some rain on Monday and Tuesday?

A. 12.5%
B. 40%
C. 50%
D. 60%
E. 67.5%
We can use the following formula:

100 = rain on Monday + rain on Tuesday - rain on both + rain on neither

100 = 70 + 65 - both + 25

Both = 60

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Jeffrey Miller Head of GMAT Instruction

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