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Age category

by rsarashi » 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

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by DavidG@VeritasPrep » Tue Mar 07, 2017 9:09 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

OAA
If there are 161 employees, the median employee would be the 81st, if we listed them in ascending order of age. (There's be 80 younger and 80 older.) Clearly the 81st oldest employee wouldn't be among the first 29. But by the time we complete the second category, ages 20 - 29, we'd have counted 87 employees. (29 + 58 = 87,) so she'll have to be in this range. The answer is A
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by [email protected] » Tue Mar 07, 2017 10:41 am
Hi rsarashi,

The "median" of a group of numbers is the "middle number" (once you put the individual numbers in order from least to greatest). Since we know that there are 161 employees, the employee who is 81st "in line" (by age) will be the median. At this point, we can either "count down" the list or "count up" the list to find the 81st employee (you'll likely find it easiest to count down though).

The first group has 29 employees; the second group has 58.... At this point, we've accounted for 29+58 = 87 employees, so the 81st employee MUST be in the second grouping.

Final Answer: A

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by Jay@ManhattanReview » 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
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