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555-605 (Medium)|   Statistics and Sets Problems|                  
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tirthshah2013
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Last year members of a certain professional organization for teachers 01 Nov 2022, 06:19
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Bunuel
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


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This question can be solved in 2 ways, Either you use approximation and get a direct answer, or get an accurate answer and find the closest one

Given - there are 49 school districts and 9.8 schools per district and 22 teachers per school, so total teachers = 49*9.8*22

Now if we approximate - we get 5*10*10*10*2 (49 ~ 50 = 5*10, 9.8 ~ 10 and 22 ~ 20= 2*10)
So we get 10*10*10*10 = 10^4.

If we directly multiply 49*9.8*22 we get 10564.4 and the closest answer to this is 10^4.

So, both ways are straightforward forward we just have a bit more calculation in the second one.

Hope it helps!!!
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Last year members of a certain professional organization for teachers 22 Dec 2023, 23:54
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2023-12-22 22_55_42-Example #2_ ROUND when it says _closest to_! _Last year members of a certain pro.png
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Last year members of a certain professional organization for teachers 30 Sep 2024, 08:29
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An easy and quick way to solve it

* first realize that it looking for approximation. It mentioned in the prompt "closest to the total number"

There are 49 school districts with 9.8 schools per district = 49 * 10 = 490 which equals to roughly 500 schools across all districts.

Now, since we are given the average number of teachers at all schools who are members of the professional organization which equals 22

Multiply 22*500 ( total number of schools) which will give 11000. Since all the answer in the form of 10^x

The answer will be D
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Last year members of a certain professional organization for teachers 14 Oct 2025, 03:35
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This problem can feel a bit overwhelming with all the layers of information, but once you see the structure, it becomes much more manageable. Let me walk you through how to approach this systematically.

Understanding What We're Dealing With

Here's what you need to see first: this problem has a three-level hierarchy. Think of it like this:
  • 49 districts
  • Each district has an average of 9.8 schools
  • Each school has an average of 22 teacher members

Your goal is to find the total number of teacher members across all these districts and schools.

Now, here's a critical insight: notice how the answer choices range from \(10^3\) to \(10^7\) – they're orders of magnitude apart! This is your signal that the problem wants you to approximate rather than calculate exact values. This makes your life much easier.

Let's Break Down the Calculation

Step 1: Find the total number of schools

You need to multiply districts by schools per district:
\(49 \times 9.8 = ?\)

Since we're looking for an order of magnitude and 9.8 is very close to 10, let's approximate:
\(49 \times 10 = 490\) schools

(The exact answer would be \(49 \times 9.8 = 480.2\), so our approximation of 490 is actually very close.)

Step 2: Find the total number of teachers

Now multiply total schools by teachers per school:
\(490 \times 22 = ?\)

Let's think about this smartly. We can approximate 22 as 20 to make the math easier:
\(490 \times 20 = 9,800\)

If you want to be slightly more precise:
\(490 \times 22 = 10,780\)

Either way, you're getting a number around 10,000.

Step 3: Match to the answer choices

Let's see which power of 10 is closest to our result of approximately 10,000:
  • \(10^7 = 10,000,000\) (way too big)
  • \(10^6 = 1,000,000\) (too big)
  • \(10^5 = 100,000\) (too big)
  • \(10^4 = 10,000\) (this matches!)
  • \(10^3 = 1,000\) (too small)

Answer: D (\(10^4\))

The Key Takeaway

The "aha moment" here is recognizing that when answer choices are powers of 10 spread far apart, you should focus on smart approximation rather than exact calculation. Round 9.8 to 10, round 22 to 20, and the arithmetic becomes much simpler while still giving you the right order of magnitude.

Want to Master This Question Type?

You can learn the systematic approach that works for all approximation and order-of-magnitude problems here on Neuron, where you'll discover when to approximate versus when to calculate exactly, plus the common variations of this problem type. You can also access comprehensive solutions for other official questions on Neuron with detailed analytics to identify and strengthen your weak areas.

Hope this helps! Feel free to ask if you have any questions.
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