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Source: — Problem Solving |
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by force5 » Sun Apr 24, 2011 4:47 am
means 8th integer should be the median.

lets plug value's

if 50 is the largest integer then smallest will be 25 ( as range is 25) hence Median cannot be 25

if 43 is the largest integer then smallest is 18. which means the median can still be 25. (pick the choice) . since this is the largest value from the answer choice this should be your answer.
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by GMATGuruNY » Sun Apr 24, 2011 5:01 am
baladon99 wrote:There are 15 different integers with their median as 25. The range of the set is 25. What could be the maximum integer in the set ?

A) 32

B) 37

C) 40

D) 43

E) 50

Ans : D
Range = greatest - smallest.
Thus, greatest = smallest + range.
To maximize the greatest integer, we need to maximize the smallest integer.

Since there are 15 integers and the median is 25, 7 integers are less than 25.
The greatest possible values are 18,19,20,21,22,23,24.
Since the smallest value cannot be greater than 18, the maximum possible value in the set = 18 + range = 18+25 = 43.

The correct answer is D.
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by Ian Stewart » Sun Apr 24, 2011 11:06 am
baladon99 wrote:There are 15 different integers with their median as 25. The range of the set is 25. What could be the maximum integer in the set ?

A) 32

B) 37

C) 40

D) 43

E) 50

Ans : D
Surely that's not how the question is worded; if that is the original wording, throw the book away and find a better one. If the question is 'What could be the maximum integer in the set', then several of the answer choices are correct. For example, 37 *could* be the maximum integer in the set if the set is {12, 13, 14, 15, 16, 17, 18, 25, 26, 27, 28, 29, 30, 31, 37}.

Instead, based on the answer given, the question means to be asking:

The median of a set of 15 distinct integers is 25. If the range of this set is 25, what is the largest possible value of the largest element in the set?

in which case the solutions above are good.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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