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In a particular state, 70 percent of the counties received some rain

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

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New post 11 Jul 2017, 03:14
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A
B
C
D
E

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  15% (low)

Question Stats:

89% (01:30) correct 11% (02:24) wrong based on 106 sessions

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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%

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

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New post 11 Jul 2017, 03:33
M=75
T= 65
Not M and T = 25
Via venn Diagram
Let both M and T = x
only M= 70-x
only T= 64-x
So, 70-x+x+64-x+25= 100
x= 60
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Re: In a particular state, 70 percent of the counties received some rain  [#permalink]

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New post 11 Jul 2017, 03:35
Let there be 100 counties in the state.

{Mon & Tue}:- {Mon} + {Tue} - {Mon & Tue} + NOT{Mon & Tue} = 100.

70 + 65 - {Mon & Tue} + 25 = 100
{Mon & Tue} = 160-100 = 60. Ans - D.
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Re: In a particular state, 70 percent of the counties received some rain  [#permalink]

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New post 11 Jul 2017, 10:00
my answer is D.

M - 70%
T- 65%
sum - 135% , overlap 35%

Neither is 25% , hence overlap is 60% ---> Option D

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

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New post 12 Jul 2017, 00:06
using venn diagrams will be of great help to solve such questions..
mon + tue - (mon and tue) + neither = 100

70 + 65 - (mon& tue) +25 = 100

solving gives 60

ans D
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Re: In a particular state, 70 percent of the counties received some rain  [#permalink]

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New post 12 Jul 2017, 03:38
Percent problem, so I assumed total counties to be 100

Just plug in the information in the expression:

Total= A+B- Both+Neither
100= 70+65-Both+25

Both= 60
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Re: In a particular state, 70 percent of the counties received some rain  [#permalink]

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New post 12 Jul 2017, 04:24
Bunuel 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%


Percentage of counties received rain on Monday = 70%
Percentage of counties received rain on Tuesday = 65%

Percentage of counties which had no rain fall = 25%
So Percentage of counties which had rainfall = 75%

So counties which had rainfall on both day = 70% + 65 % - 75% = 60%

Answer D
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Re: In a particular state, 70 percent of the counties received some rain  [#permalink]

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New post 12 Jul 2017, 17:16
Bunuel 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

Answer: D
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Re: In a particular state, 70 percent of the counties received some rain   [#permalink] 12 Jul 2017, 17:16
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