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Last year members of a certain professional organization for teachers

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Last year members of a certain professional organization for teachers  [#permalink]

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New post 01 Aug 2018, 10:30
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Question Stats:

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Last year members of a certain professional organization for teachers consisted of teachers from 49 different school districts, with an average (arithmetic mean) of 9.8 schools per district. Last year the average number of teachers at these schools who were members of the organization was 22. Which of the following is closest to the total number of members of the organization last year?

A. 10^7
B. 10^6
C. 10^5
D. 10^4
E. 10^3

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Re: Last year members of a certain professional organization for teachers  [#permalink]

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New post 01 Aug 2018, 23:28
Bunuel wrote:
Last year members of a certain professional organization for teachers consisted of teachers from 49 different school districts, with an average (arithmetic mean) of 9.8 schools per district. Last year the average number of teachers at these schools who were members of the organization was 22. Which of the following is closest to the total number of members of the organization last year?

A. 107
B. 106
C. 105
D. 104
E. 103

NEW question from GMAT® Quantitative Review 2019


(PS12450)


Pls provide solution to this problem. I thought it to be simple average question and multiplied all the figures as
1) Total schools = Average schools per districts x Number of districts = 9.8 x 49
2) Total number of members of the organization = Average number of teachers at each schools x Total Schools = (9.8 x 49) x 22

It gave huge number.. :(.
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Re: Last year members of a certain professional organization for teachers  [#permalink]

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New post 02 Aug 2018, 22:22
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The number of schools do not result a whole number from the given info. Pls check the question

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Re: Last year members of a certain professional organization for teachers  [#permalink]

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New post 02 Aug 2018, 22:28
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Re: Last year members of a certain professional organization for teachers  [#permalink]

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New post 02 Aug 2018, 22:35
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We have 49 districts with average of 9.8 schools in one district, with 22 teachers from each school. So, we have 49*9.8*22=5*10*10*10*2=10^3(5*2)=10^4 (D)
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Re: Last year members of a certain professional organization for teachers  [#permalink]

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New post 03 Aug 2018, 05:52
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Bunuel wrote:
Last year members of a certain professional organization for teachers consisted of teachers from 49 different school districts, with an average (arithmetic mean) of 9.8 schools per district. Last year the average number of teachers at these schools who were members of the organization was 22. Which of the following is closest to the total number of members of the organization last year?

A. 10^7
B. 10^6
C. 10^5
D. 10^4
E. 10^3

NEW question from GMAT® Quantitative Review 2019


(PS12450)


Total no of schools=Avg. no of schools per district*Total no of districts=9.8*49
Total no of members=Avg. no. of teachers per school*Total no of schools=\(49*(9.8*22)= (\approx{50})*(\approx{10})*(\approx{20})=10^4\)

Ans. (D)
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Re: Last year members of a certain professional organization for teachers  [#permalink]

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New post 07 Aug 2018, 18:50
tatz wrote:
Bunuel wrote:
Last year members of a certain professional organization for teachers consisted of teachers from 49 different school districts, with an average (arithmetic mean) of 9.8 schools per district. Last year the average number of teachers at these schools who were members of the organization was 22. Which of the following is closest to the total number of members of the organization last year?

A. 107
B. 106
C. 105
D. 104
E. 103

NEW question from GMAT® Quantitative Review 2019


(PS12450)


Pls provide solution to this problem. I thought it to be simple average question and multiplied all the figures as
1) Total schools = Average schools per districts x Number of districts = 9.8 x 49
2) Total number of members of the organization = Average number of teachers at each schools x Total Schools = (9.8 x 49) x 22

It gave huge number.. :(.


I solved this question by rounding it off to the nearest integer values i.e. 10*50*22. i.e. 11000 and the nearest value of 11000 is 10000 i.e. 10^4.
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Re: Last year members of a certain professional organization for teachers  [#permalink]

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New post 10 Aug 2018, 17:35
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Bunuel wrote:
Last year members of a certain professional organization for teachers consisted of teachers from 49 different school districts, with an average (arithmetic mean) of 9.8 schools per district. Last year the average number of teachers at these schools who were members of the organization was 22. Which of the following is closest to the total number of members of the organization last year?

A. 10^7
B. 10^6
C. 10^5
D. 10^4
E. 10^3


Since there are 49 districts and an average of 9.8 schools per district, there are 49 x 9.8 schools in total. Furthermore, since there are on average 22 teachers per school, the total number of teachers is 49 x 9.8 x 22, which is approximately 50 x 10 x 22 = 11,000. We see that this is closest to 10^4.

Answer: D
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Re: Last year members of a certain professional organization for teachers  [#permalink]

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New post 15 Aug 2018, 21:31
Hi,
Total number of schools in 49 Districts/ number of districts= Avg Schools Per district.
So
Total number of schools in 49 Districts / 49= 9.8,
=>total number of schools in 49 districts is 49*9.8 or 50 *10=500 { rounding 9.8 to 10 and rounding 49 to 50}

Now total number teachers in the 49 school/ total number of schools = Avg teacher per school

Total number of teachers in 49 schools= 500*22 or 500*20=10000 which is 10^4

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Re: Last year members of a certain professional organization for teachers  [#permalink]

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New post 17 Aug 2018, 00:43

Solution


Given:
    • Last year, certain professional organization consisted of teachers from 49 different school districts
    • Average number of schools per district = 9.8
    • Average number of teachers, at these schools, who were members of the organization = 22

To find:
    • Which of the given answer choices is closest to the total number of members of the organization last year

Approach and Working:
    • Average number of schools per district = total number of schools/ total number of districts.
      o Implies, total number of schools = total number of districts * average number of schools per district
      o Thus, total number of schools = 49 x 9.8
    • And, average number of teachers at these schools, who were members = total number of teachers, who were members/total number of schools
      o Implies, total number of members of organization = average number of teachers at these schools, who were members * total number of schools
      o Thus, the total number of members of organization = (49 x 9.8) x 22 ≃ 50 x 10 x 20 = \(10^4\)

Therefore, the total number of members of the organization last year = 104

Hence, the correct answer is option D.

Answer: D

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Re: Last year members of a certain professional organization for teachers  [#permalink]

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New post 17 Aug 2018, 09:13
9.8 schools/district * 49 district * 22 teachers/school
Round to 10*50*20=10,000=10^4
Answer D
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Re: Last year members of a certain professional organization for teachers  [#permalink]

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New post 24 Sep 2018, 20:48
total number of members=49*10(approx of 9.8)*22=490*22=490*20(approx)=9800=10^4 (approx)
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Re: Last year members of a certain professional organization for teachers  [#permalink]

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New post 03 Nov 2018, 06:12
tatz wrote:
Bunuel wrote:
Last year members of a certain professional organization for teachers consisted of teachers from 49 different school districts, with an average (arithmetic mean) of 9.8 schools per district. Last year the average number of teachers at these schools who were members of the organization was 22. Which of the following is closest to the total number of members of the organization last year?

A. 107
B. 106
C. 105
D. 104
E. 103

NEW question from GMAT® Quantitative Review 2019


(PS12450)


Pls provide solution to this problem. I thought it to be simple average question and multiplied all the figures as
1) Total schools = Average schools per districts x Number of districts = 9.8 x 49
2) Total number of members of the organization = Average number of teachers at each schools x Total Schools = (9.8 x 49) x 22

It gave huge number.. :(.


Answer: We can solve it by rounding off the numbers

Total members(teachers) = Total school districts * Total school per district * avg teacher per school
= 49 * 9.8 * 22

Now since the options in the original question question are given in terms of power of ten, so
Total teachers = 50 * 10 * 2*10 = 5*2*10^3 = 10^4
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Re: Last year members of a certain professional organization for teachers &nbs [#permalink] 03 Nov 2018, 06:12
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