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In a particular state, 70% of the counties received some rain on Monda

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In a particular state, 70% of the counties received some rain on Monda [#permalink]

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New post 20 Mar 2010, 11:41
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A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

88% (00:49) correct 13% (00:42) wrong based on 16 sessions

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In a particular 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 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%
[Reveal] Spoiler: OA

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Re: In a particular state, 70% of the counties received some rain on Monda [#permalink]

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New post 20 Mar 2010, 13:29
changhiskhan wrote:
In a particular 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 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%


Percent of countes in which it rained = percent of counties in which it rained on monday + percent of counties in which it rained on tuesday - percent of counties in which it rained both days

100 -25 = 70+65 - percent of counties in which it rained both days
percent of counties in which it rained both days = 135 - 75 = 60
hence D is the answer
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Re: In a particular state, 70% of the counties received some rain on Monda [#permalink]

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New post 20 Mar 2010, 16:53
changhiskhan wrote:
In a particular 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 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%


So, 25% of the counties received rain neither on Monday nor Tuesday. Thus 75% of the counties received rain either Monday or Tuesday.

We know that 70% of the counties received some rain on Monday. Then it has to be that 5% of the counties that did not receive any rain on Monday received some rain on Tuesday in order to make it to 75%. What this tells us is that, of the 65% of the counties that received rain on Tuesday, 5% received rain only on Tuesday and 60% of the counties received rain on Monday.

D
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Re: In a particular state, 70% of the counties received some rain on Monda [#permalink]

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New post 20 Mar 2010, 17:29
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Since this question involves percent, I would begin by saying there are 100 total counties.

I'd then use the formula:

group1+group2-both+neither = total

In which
group1 = counties that received rain on Monday = 70
group2 = counties that received rain on Tuesday = 65
neither = counties that had no rain either day = 25
both = the unknown quantity we are solving for

therefore

70 + 65 - both + 25 = 100
both = 60

therefore,

60/100 counties received rain on both days.

Answer D

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Re: In a particular state, 70% of the counties received some rain on Monda [#permalink]

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New post 15 Nov 2017, 06:10
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Re: In a particular state, 70% of the counties received some rain on Monda   [#permalink] 15 Nov 2017, 06:10
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