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Which of the following could be the median for a set of

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Which of the following could be the median for a set of

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Which of the following could be the median for a set of integers {97, 98, 56, x, 86}, given that 20 < x < 80?

A. 71
B. 86
C. 91.5
D. 97
E. 397.5

OA B

Source: Princeton Review

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BTGmoderatorDC wrote:
Which of the following could be the median for a set of integers {97, 98, 56, x, 86}, given that 20 < x < 80?

A. 71
B. 86
C. 91.5
D. 97
E. 397.5

OA B

Source: Princeton Review
If 20 < x ≤ 56, then in ascending order, the list of numbers is:

x, 56, 86, 97, 98.

We see that the median is 86.

If 56 ≤ x < 80, then in ascending order, the list of numbers is:

56, x, 86, 97, 98.

We see that the median is 86.

Answer: B

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There are 2 scenarios for the given set of integers since \(20 < x < 80\).

1. \(20 < x < 56\), Arranging in ascending order, {x,56,86,97,98}, we have median \(= 86\).

2. \(56 \leq x < 80\), Arranging in ascending order, {56,x,86,97,98}, we have median \(= 86\).

Therefore, the correct option is __B__

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BTGmoderatorDC wrote:
Which of the following could be the median for a set of integers {97, 98, 56, x, 86}, given that 20 < x < 80?

A. 71
B. 86
C. 91.5
D. 97
E. 397.5
Since 20 < x < 80, we can see that, if we arrange the 5 numbers in ASCENDING order, we get two possible cases:
case a: {x, 56, 86, 97, 98}
case b: {56, x, 86, 97, 98}

In both cases, the median is 86

Answer: B

Cheers,
Brent

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Brent Hanneson – Creator of GMATPrepNow.com
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