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Which of the following is closest to the percent of all the people sur

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Which of the following is closest to the percent of all the people sur  [#permalink]

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16 Dec 2019, 00:15
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45% (medium)

Question Stats:

63% (01:53) correct 37% (01:45) wrong based on 35 sessions

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Which of the following is closest to the percent of all the people survey who indicated the Internet as their preferred method to obtain news?

A. 18.8%
B. 21.7%
C. 23.0%
D. 33.3%
E. 46.0%

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Re: Which of the following is closest to the percent of all the people sur  [#permalink]

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21 Jan 2020, 02:26
1
First we calculate the number of people who chose internet in each group
1. GROUP 20-49
35% of 240: 10% of 240 is 24, so 30% is 72 and 35% is 84.
2. GROUP 50 AND OLDER
11% of 300 is straight up 33.

Sum A) the people who chose internet in both the groups and B) total people in survey.
Now calculate percent of people who chose internet.
(117/540)% = 21.something%
This can be calculated using the same method as mentioned for group A

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Re: Which of the following is closest to the percent of all the people sur  [#permalink]

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21 Jan 2020, 03:29
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We have two groups, one with a 35% average, one with an 11% average. If the groups were equal in size, then combined they would have a (35+11)/2 = 23% average. But the 11% group is very slightly bigger than the 35% group, so the overall average will be slightly closer to 11%. Only answer B makes much sense, though I suppose if you were undecided between A and B you might do a bit of calculation.
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Re: Which of the following is closest to the percent of all the people sur  [#permalink]

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21 Jan 2020, 03:40
IanStewart wrote:
We have two groups, one with a 35% average, one with an 11% average. If the groups were equal in size, then combined they would have a (35+11)/2 = 23% average. But the 11% group is very slightly bigger than the 35% group, so the overall average will be slightly closer to 11%. Only answer B makes much sense, though I suppose if you were undecided between A and B you might do a bit of calculation.

Could you please explain "so the overall average will be slightly closer to 11%"?

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21 Jan 2020, 03:44
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TSneha wrote:
Could you please explain "so the overall average will be slightly closer to 11%"?

It's just a weighted average problem. Using simpler numbers, say you mix a 20% salt solution with a 40% salt solution. If you use equal quantities of each, the mixture will be 30% salt. If you use more of the 20% solution, the resulting mixture will be closer to 20% salt (so will be between 20% and 30% salt). The ratio of the amounts you use determine where the overall average ends up.
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Re: Which of the following is closest to the percent of all the people sur  [#permalink]

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21 Jan 2020, 08:28
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Shortcut:
Ratio of people in both the groups = 240:300 = 4:5
Now you are mixing them.
Therefore by weighted avg approach

No of people choosing internet as an option = ((35*4) +(11*5))/9
= 21.7

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Re: Which of the following is closest to the percent of all the people sur  [#permalink]

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23 Jan 2020, 09:02
1
Bunuel wrote:

Which of the following is closest to the percent of all the people survey who indicated the Internet as their preferred method to obtain news?

A. 18.8%
B. 21.7%
C. 23.0%
D. 33.3%
E. 46.0%

Because the number of individuals in each of the two groups is different (240 versus 300), we have to calculate two separate values. For age group 20 to 49, we see that 240 x 0.35 = 84 individuals prefer the internet for obtaining news; for age group 50 and older, we see that 300 x 0.11 = 33 individuals prefer the internet for obtaining news. Therefore, the overall percent who prefer the internet is:

(0.35 x 240 + 300 x 0.11)/(240 + 300) = 117/540 ≈ 0.217 = 21.7%

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Re: Which of the following is closest to the percent of all the people sur   [#permalink] 23 Jan 2020, 09:02
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