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Math Expert V
Joined: 02 Sep 2009
Posts: 57238
Which of the following could be the median for a set of integers {97,  [#permalink]

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Difficulty:   5% (low)

Question Stats: 80% (00:59) correct 20% (01:16) wrong based on 51 sessions

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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

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Posts: 3018
Re: Which of the following could be the median for a set of integers {97,  [#permalink]

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Solution

Given:
• A set of integers = {97, 98, 56, x, 86}
• 20 < x < 80

To find:
• The median of the given set of integers

Approach and Working:
• As there are 5 terms in the set, the median will be the 3rd term in the series, sorted in ascending or descending order
• Also, because 20 < x < 80, the least 2 terms will be always x and 56, in any order
• Hence, the mid-term = 3rd term = 86

Hence, the correct answer is option B.

Answer: B
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Which of the following could be the median for a set of integers {97,  [#permalink]

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Bunuel 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

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

Ans. (B)
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Re: Which of the following could be the median for a set of integers {97,  [#permalink]

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Top Contributor
Bunuel 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 we're told x is an INTEGER, we can eliminate C and E

Rearrange KNOWN values in ascending order: {56, 86, 97, 98}

At this point, we can see that, if x is some number between 56 and 86, the median will be 86

For example, if x = 60, then the set becomes {56, 60, 86, 97, 98}
Median = 86

Answer: B

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Re: Which of the following could be the median for a set of integers {97,  [#permalink]

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Bunuel 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

set of integers wont have optins c & e

so re arranging set ( 56,86,x,97,98)

only value which goes correct is B 86 .
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Re: Which of the following could be the median for a set of integers {97,  [#permalink]

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Bunuel 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

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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Re: Which of the following could be the median for a set of integers {97,  [#permalink]

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Bunuel 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

tow possible positions of x (Marked in RED)

x 56 x 86 97 98

In either case, 86 is the median.
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I never gave up what I wanted- Re: Which of the following could be the median for a set of integers {97,   [#permalink] 17 Jun 2019, 17:56
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