Last year members of a certain professional organization for teachers

The number of schools do not result a whole number from the given info. Pls check the question

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Exponent signs were missing. Edited. Thank you.

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)

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.

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

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

Probus

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

9.8 schools/district * 49 district * 22 teachers/school
Round to 10*50*20=10,000=10^4
Answer D

total number of members=49*10(approx of 9.8)*22=490*22=490*20(approx)=9800=10^4 (approx)

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

I rounded these numbers and then factored them. Came up with a very quick solution.

49 Districts | 9.8 Schools | 22 Teachers

Step 1) Round

50 Districts | 10 Schools | 20 Teachers

Step 2) Factor to easy numbers

5 * 10 | 10 | 10 * 2

Step 3) Multiply

\(10^3\) * 5*2 = \(10^4\)

the question requires some heavy calculation. How to handle it under 2 mins?

D.

Total # of schools = Total # of districts * Average # of schools per district
= 49 * 9.9 ~ 50 * 10 = 500

Total # of members = Total # of schools * Avg # of teachers
= 500 * 22 ~ 500 * 20 = 10000 i.e. 10^4

\(49*9.8*22\)

\(Now \ approximating, \ 50*10*20\)

\(=10,000\)

\(=10^4\)

The answer is D

A question that is so obviously a candidate for ballparking, even the answer explanation in the OG does it that way...one of only two questions that GMAC shows ballparking in the 2022 OG Quant. By my count, of the 212 PS questions in that edition, 26 are ballparking candidates, and they cover a wide variety of math concepts. Ballparking is probably the single most useful technique on Quant (okay, maybe AD/BCE, but everybody knows that ).

ThatDudeKnowsBallparking

I'm not gonna explain anything different from what others have above and will simplify the calculations.
(I believe a lot of you already have done this but nonetheless let's proceed)

So it states that 49 school districts have an average of 9.8 schools per district.
Now instead of calculating 49 x 9.8 you could have very simply gone with either 49 x 10 = 490 schools or 50 x 10 = 500 schools.

Next it says that 22 teachers per school on average. So instead of multiplying 22 by 490 schools or 500 schools.

Simply equate 22 teachers to 25 teachers.

Now multiple these 25 teachers by 500 schools = 12,500 teachers.

Although this answer is ahead of the actual answer it is still in the lower spectrum based on the options provided.
Moreover the question asks us "close to which" and hence you can go with the answer as 10^4 or Option D.

The question asks for "members".

If we round the numbers, we have 50 districts * 10 schools/district * 20 members/school = 10,000 members