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If \(x\) is a positive integer, what is the median of the set of consecutive integers from \(1\) to \(x\) inclusive?

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If \(x\) is a positive integer, what is the median of the set of consecutive integers from \(1\) to \(x\) inclusive?

by VJesus12 » Fri Feb 19, 2021 7:22 am

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If \(x\) is a positive integer, what is the median of the set of consecutive integers from \(1\) to \(x\) inclusive?

(1) The average of the set of integers from \(1\) to \(x\) inclusive is \(11.\)

(2) The range of the set of integers from \(1\) to \(x\) inclusive is \(20.\)

Answer: D

Source: Manhattan GMAT
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Source: — Data Sufficiency |
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Re: If \(x\) is a positive integer, what is the median of the set of consecutive integers from \(1\) to \(x\) inclusive?

by deloitte247 » Sun Feb 28, 2021 2:14 am

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Target question: what is the median of the set of consecutive integers from 1 to x inclusive?

Statement 1: The average of the set of integers from 1 to x inclusive is 11.
For any set of corrective integer, the mean is equal to median.
Since average = mean, then average = median
Median = 11
Statement 1 is SUFFICIENT

Statement 2: The range of the set of integers from 1 to X inclusive is 20.
Range = largest term - smallest term
Let the largest term = a, smallest term = 1
a - 1 = 20 and a = 20+1 = 21
So, the set of consecutive integers are; 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21.
Median = 11
Statement 2 is also SUFFICIENT.

Since each statement alone is SUFFICIENT, option D is the correct answer.
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