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Age category

This topic has 4 expert replies and 0 member replies
rsarashi Master | Next Rank: 500 Posts Default Avatar
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Age category

Post Tue Mar 07, 2017 8:59 am
Age category Number of Employees
(in years)
Less than 20 29
20-29 58
30-39 36
40-49 21
50-59 10
60-69 5
70 and over 2


The table above gives the age categories of the 161 employees at Company X and the number of employees in each category. According to the table, if m is the median age, in years, of the employees at Company X, then m must satisfy which of the following?

A) 20 ≤ m ≤ 29
B) 25 ≤ m ≤ 34
C) 30 ≤ m ≤ 39
D) 35 ≤ m ≤ 44
E) 40 ≤ m ≤ 49

OAA

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Post Fri Dec 08, 2017 7:10 am
rsarashi wrote:
Age category Number of Employees
(in years)
Less than 20 29
20-29 58
30-39 36
40-49 21
50-59 10
60-69 5
70 and over 2


The table above gives the age categories of the 161 employees at Company X and the number of employees in each category. According to the table, if m is the median age, in years, of the employees at Company X, then m must satisfy which of the following?

A) 20 ≤ m ≤ 29
B) 25 ≤ m ≤ 34
C) 30 ≤ m ≤ 39
D) 35 ≤ m ≤ 44
E) 40 ≤ m ≤ 49
We are given a table that has the age categories of the 161 employees at Company X and the number of employees in each category. Recall that if we have a set of n numbers arranged in order, the median of this set of n numbers is the number at the [(n + 1)/2]th position. Thus, the employee with the median age is at the (161+1)/2 = 162/2 = 81st position (assuming the ages of the employees are listed in order). The table provides us with the following information:

Age less than 20: 29 employees (i.e., 1st data point to 29th data point)

Age 20-29: 58 employees (i.e., 30th data point to 87th data point)

We see that the 81st data point will fall into the age group from 20-29 since this age group contains the 30th data point to the 87th data point.

Thus 20 ≤ m ≤ 29.

Answer: A

_________________

Scott Woodbury Stewart Founder & CEO
GMAT Quant Self-Study Course - 500+ lessons 3000+ practice problems 800+ HD solutions
5-Day Free Trial 5-DAY FREE, FULL-ACCESS TRIAL TTP QUANT

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Top Reply
Post Tue Mar 07, 2017 9:57 pm
rsarashi wrote:
Age category (in years)
Number of Employees
Less than 20 29
20-29 58
30-39 36
40-49 21
50-59 10
60-69 5
70 and over 2


The table above gives the age categories of the 161 employees at Company X and the number of employees in each category. According to the table, if m is the median age, in years, of the employees at Company X, then m must satisfy which of the following?

A) 20 ≤ m ≤ 29
B) 25 ≤ m ≤ 34
C) 30 ≤ m ≤ 39
D) 35 ≤ m ≤ 44
E) 40 ≤ m ≤ 49

OAA
Hi rsarashi,

We have to find out the age category the median age of 161 employees belongs to. The median of 161 employees would be the middle-most number = (161 + 1)/2 = 81. Thus, the age of the 81st employee, provided the age categories are arranged in ascending order, would be the median.

So, we must first arrange the age categories in an ascending order. We see that they are already done.

We can make another column "Cumulative number of employees," and find out in which age category 81 lies. That age category would be the median age category and the answer. "Cumulative number of employees" for each age category can be achieved by adding the number of employees of all the previous age categories.

Age category / # of Emp. / Cumulative # of Emp.

< 20: 29: 29
20-29: 58: (29 + 58) = 87 <-- 81 = median lies in the age category 20-29. The correct answer is A.
30-39: 36
40-49: 21
50-59: 10
60-69: 5
> 70: 2

The correct answer: A

Hope this helps!

Relevant book: Manhattan Review GMAT Sets & Statistics Guide

-Jay
_________________
Manhattan Review GMAT Prep

Locations: New York | Beijing | Auckland | Milan | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

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Thanked by: rsarashi

GMAT/MBA Expert

Post Fri Dec 08, 2017 7:10 am
rsarashi wrote:
Age category Number of Employees
(in years)
Less than 20 29
20-29 58
30-39 36
40-49 21
50-59 10
60-69 5
70 and over 2


The table above gives the age categories of the 161 employees at Company X and the number of employees in each category. According to the table, if m is the median age, in years, of the employees at Company X, then m must satisfy which of the following?

A) 20 ≤ m ≤ 29
B) 25 ≤ m ≤ 34
C) 30 ≤ m ≤ 39
D) 35 ≤ m ≤ 44
E) 40 ≤ m ≤ 49
We are given a table that has the age categories of the 161 employees at Company X and the number of employees in each category. Recall that if we have a set of n numbers arranged in order, the median of this set of n numbers is the number at the [(n + 1)/2]th position. Thus, the employee with the median age is at the (161+1)/2 = 162/2 = 81st position (assuming the ages of the employees are listed in order). The table provides us with the following information:

Age less than 20: 29 employees (i.e., 1st data point to 29th data point)

Age 20-29: 58 employees (i.e., 30th data point to 87th data point)

We see that the 81st data point will fall into the age group from 20-29 since this age group contains the 30th data point to the 87th data point.

Thus 20 ≤ m ≤ 29.

Answer: A

_________________

Scott Woodbury Stewart Founder & CEO
GMAT Quant Self-Study Course - 500+ lessons 3000+ practice problems 800+ HD solutions
5-Day Free Trial 5-DAY FREE, FULL-ACCESS TRIAL TTP QUANT

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Post Tue Mar 07, 2017 9:57 pm
rsarashi wrote:
Age category (in years)
Number of Employees
Less than 20 29
20-29 58
30-39 36
40-49 21
50-59 10
60-69 5
70 and over 2


The table above gives the age categories of the 161 employees at Company X and the number of employees in each category. According to the table, if m is the median age, in years, of the employees at Company X, then m must satisfy which of the following?

A) 20 ≤ m ≤ 29
B) 25 ≤ m ≤ 34
C) 30 ≤ m ≤ 39
D) 35 ≤ m ≤ 44
E) 40 ≤ m ≤ 49

OAA
Hi rsarashi,

We have to find out the age category the median age of 161 employees belongs to. The median of 161 employees would be the middle-most number = (161 + 1)/2 = 81. Thus, the age of the 81st employee, provided the age categories are arranged in ascending order, would be the median.

So, we must first arrange the age categories in an ascending order. We see that they are already done.

We can make another column "Cumulative number of employees," and find out in which age category 81 lies. That age category would be the median age category and the answer. "Cumulative number of employees" for each age category can be achieved by adding the number of employees of all the previous age categories.

Age category / # of Emp. / Cumulative # of Emp.

< 20: 29: 29
20-29: 58: (29 + 58) = 87 <-- 81 = median lies in the age category 20-29. The correct answer is A.
30-39: 36
40-49: 21
50-59: 10
60-69: 5
> 70: 2

The correct answer: A

Hope this helps!

Relevant book: Manhattan Review GMAT Sets & Statistics Guide

-Jay
_________________
Manhattan Review GMAT Prep

Locations: New York | Beijing | Auckland | Milan | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

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Thanked by: rsarashi

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