Statistics and Sets Problems

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swerve: Legendary Member; Posts: 2499; Joined: Sun Oct 29, 2017 2:04 pm; Followed by:6 members

Statistics and Sets Problems

by swerve » Mon Apr 13, 2020 12:01 pm

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Set \(S\) consists of consecutive positive integers. If the lowest integer in Set \(S\) is \(1\) and the sum of the integers os Set \(S\) is 231, what is the median of Set \(S\)?

A. 10.5
B. 11
C. 12
D. 13
E. 22

The OA is B

Source: Magoosh

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Source: Beat The GMAT — Problem Solving | Mon Apr 13, 2020 12:01 pm

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

Re: Statistics and Sets Problems

by Scott@TargetTestPrep » Fri Apr 17, 2020 3:40 am

swerve wrote: ↑
Mon Apr 13, 2020 12:01 pm
Set \(S\) consists of consecutive positive integers. If the lowest integer in Set \(S\) is \(1\) and the sum of the integers os Set \(S\) is 231, what is the median of Set \(S\)?

A. 10.5
B. 11
C. 12
D. 13
E. 22

The OA is B

Source: Magoosh

If we let x = the largest integer in set S, we can create the following equation using the formula average * quantity = sum:

(1 + x)/2 * (x - 1 + 1) = 231

(1 + x)/2 * x = 231

x + x^2 = 462

x^2 + x - 462 = 0

(x + 22)(x - 21) = 0

x = -22 and x = 21

Since x is positive, x = 21. Since the median of set S is also the average of set S, the median of set S is (1 + 21)/2 = 22/2 = 11.

Answer: B

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