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A survey of n people in the town of Eros found that 50% of them prefer

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DensetsuNo
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A survey of n people in the town of Eros found that 50% of them prefer [#permalink] New post   08 Jul 2016, 03:13
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A survey of n people in the town of Eros found that 50% of them preferred Brand A. Another survey of 100 people in the town of Angie found that 60% preferred Brand A. In total, 55% of all the people surveyed together preferred Brand A. What is the total number of people surveyed?

(A) 50
(B) 100
(C) 150
(D) 200
(E) 250

Source: Nova's GMAT Math Prep Course
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D
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Re: A survey of n people in the town of Eros found that 50% of them prefer [#permalink] New post   08 Jul 2016, 04:55
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DensetsuNo wrote:
A survey of n people in the town of Eros found that 50% of them preferred Brand A. Another survey of 100 people in the town of Angie found that 60% preferred Brand A. In total, 55% of all the people surveyed together preferred Brand A. What is the total number of people surveyed?

(A)50
(B)100
(C)150
(D)200
(E)250

Source: Nova's GMAT Math Prep Course

Like always: Kudos if you like.


It is simply a weighted average question. Since the given average of 50% and 60% is 55% (right in the middle), it means the number of people surveyed in Eros (n) is same as the number of people surveyed in Angie.
So n = 100
Total = 100 + 100 = 200

Answer (D)
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Re: A survey of n people in the town of Eros found that 50% of them prefer [#permalink] New post   08 Jul 2016, 05:05
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DensetsuNo wrote:
A survey of n people in the town of Eros found that 50% of them preferred Brand A. Another survey of 100 people in the town of Angie found that 60% preferred Brand A. In total, 55% of all the people surveyed together preferred Brand A. What is the total number of people surveyed?

(A)50
(B)100
(C)150
(D)200
(E)250

Source: Nova's GMAT Math Prep Course

Like always: Kudos if you like.


50% of n = .5n
60% of 100= 60

.5n+60= .55(n+100)

n= 100

And there were 100 more people from other survey, making total 200 people.

D is the answer
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Re: A survey of n people in the town of Eros found that 50% of them prefer [#permalink] New post   08 Jul 2016, 16:10
Absolutely!

50% of n people from Eros prefer brand A.
50% of n is = n/2.
60% of 100 people from Angie prefer brand A.
60% of 100 is 60.

Of the total n + 100 people surveyed, n/2 + 60 prefer brand A.
Given that this is 55%, we have:
\(\frac{\left( \frac{n}{2}+60 \right)}{\left( n+100 \right)}\cdot \; 100\; =\; 55\; ->\; n\; =\; 200\)
Answer D.

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Re: A survey of n people in the town of Eros found that 50% of them prefer [#permalink] New post   16 Aug 2020, 11:17
DensetsuNo wrote:
A survey of n people in the town of Eros found that 50% of them preferred Brand A. Another survey of 100 people in the town of Angie found that 60% preferred Brand A. In total, 55% of all the people surveyed together preferred Brand A. What is the total number of people surveyed?

(A) 50
(B) 100
(C) 150
(D) 200
(E) 250

Source: Nova's GMAT Math Prep Course


from given info
55/100 = .5n+600/n+100
solve for n = 100
and total people ; 100+100 ; 200
OPTION D
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Re: A survey of n people in the town of Eros found that 50% of them prefer [#permalink] New post   15 Jun 2023, 10:45
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Re: A survey of n people in the town of Eros found that 50% of them prefer [#permalink]
15 Jun 2023, 10:45
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