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Re: A set of 25 different integers has a median of 50 and a range of 50. W [#permalink]

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18 Sep 2011, 20:43

dreambeliever wrote:

A set of 25 different integers has a median of 50 and a range of 50. What is the greatest possible integer that could be in this set? (A) 62 (B) 68 (C) 75 (D) 88 (E) 100

I go for D

Given Median = 50 Range = 50

Let Numbers be x1 , x2 , x3 ,.....,x13, .....x24, x25 x13 = 50 x25 - x1 = 50 Now From answer choices, E : let x25 = 100 => x1 = 50 Not possible as we need atleast a difference of 12 between x13 and x1.

Applying the same for all the answer choices we get A, B, C, D are possible. As we are asked abt max possible Ans is D.

Re: A set of 25 different integers has a median of 50 and a range of 50. W [#permalink]

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18 Sep 2011, 22:29

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yes.. i think D too...

i have a different solution though... without looking at the answers...

the total set contains 25 numbers... and the mid-value (median) is 50 which implies the 13th value is 50.

For range to remain 50 and the last digit to be maximum, the first digit must be as close to 50 as possible... the greatest possible number is x1 is 38 (only then will the 13th number be 50)

Re: A set of 25 different integers has a median of 50 and a range of 50. W [#permalink]

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19 Sep 2011, 00:26

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dreambeliever wrote:

A set of 25 different integers has a median of 50 and a range of 50. What is the greatest possible integer that could be in this set? (A) 62 (B) 68 (C) 75 (D) 88 (E) 100

Sol:

50 is the 13th number in the set.

Smallest integer closest to 50= 50-12=38 {: "minus 12" because there must be exactly 12 unique integers smaller than 50(median=50):}

Re: A set of 25 different integers has a median of 50 and a range of 50. W [#permalink]

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29 Nov 2014, 23:13

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Re: A set of 25 different integers has a median of 50 and a range of 50. W [#permalink]

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30 Nov 2014, 05:18

Expert's post

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dreambeliever wrote:

A set of 25 different integers has a median of 50 and a range of 50. What is the greatest possible integer that could be in this set?

(A) 62 (B) 68 (C) 75 (D) 88 (E) 100

Consider 25 numbers in ascending order to be \(x_1\), \(x_2\), \(x_3\), ..., \(x_{25}\).

The median of a set with odd number of elements is the middle number (when arranged in ascending or descending order), so the median of given set is \(x_{13}=50\);

The range of a set is the difference between the largest and the smallest numbers of a set, so the range of given set is \(50=x_{25}-x_{1}\) --> \(x_{25}=50+x_{1}\);

We want to maximize \(x_{25}\), hence we need to maximize \(x_{1}\). Since all integers must be distinct then the maximum value of \(x_{1}\) will be \(median-12=50-12=38\) and thus the maximum value of \(x_{25}\) is \(x_{25}=38+50=88\).

The set could be {38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 88}

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