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Set of 15 integer

tagged by: Brent@GMATPrepNow

This topic has 5 expert replies and 0 member replies
paresh_patil Senior | Next Rank: 100 Posts
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Set of 15 integer

Fri Mar 15, 2013 2:26 pm
A set of 15 different integer has a median of 25 & a range of 25. What is the greatest possible integer that could be in this set?
A) 32
B) 37
C) 40
D) 43
E) 50

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Brent@GMATPrepNow GMAT Instructor
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Fri Mar 15, 2013 2:37 pm
paresh_patil wrote:
A set of 15 different integer has a median of 25 & a range of 25. What is the greatest possible integer that could be in this set?
A) 32
B) 37
C) 40
D) 43
E) 50
Let's tackle this one step at a time.

First, we have 15 different integers.
We can let these 15 spaces represent the 15 numbers written in ascending order: _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

If the median is 25, we can add this as the middle value: _ _ _ _ _ _ _ 25 _ _ _ _ _ _ _
Notice that 7 of the remaining numbers must be greater than 25 and the other 7 remaining number must be less than 25.

Since, we are told that the range is 25, we know that the greatest number minus the smallest number = 25

Now notice two things:
1) Once we know the value of the smallest number, the value of the greatest number is fixed.
For example, if the smallest number were 10, then the greatest number would have to be 35 in order to have a range of 25
Similarly, if the smallest number were 12, then the greatest number would have to be 37 in order to have a range of 25

2) If we want to maximize the value of the greatest number, we need to maximize the value of the smallest number.

So, how do we maximize the value of the smallest number in the set?
To do this, we must maximize each of the 7 numbers that are less than the median of 25.

Since the 15 numbers are all different, the largest values we can assign to the numbers less than the median of 25 are as follows:
18 19 20 21 22 23 24 25 _ _ _ _ _ _ _ (this maximizes the value of the smallest number)

If 18 is the maximum value we can assign to the smallest number, and if the range of the 15 numbers is 25, then greatest number must equal 43 (since 43 - 18 = 25)

So, the numbers are as follows: 18 19 20 21 22 23 24 25 _ _ _ _ _ _ 43 (the missing numbers don't really matter here)

This means the answer is 43 = D

Cheers,
Brent

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Anju@Gurome GMAT Instructor
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Fri Mar 15, 2013 8:30 pm
paresh_patil wrote:
A set of 15 different integer has a median of 25 & a range of 25. What is the greatest possible integer that could be in this set?
Median of a set of 15 different integers will be the 8th integer of the series when arranged according to their values.

Now, Largest - Smallest = Range ---> Largest = (Smallest + Range)
As the range is fixed, we can maximize largest number by maximizing the smallest number.

Maximum possible value of the smallest integer in the set is (25 - 7) = 18, as all the terms are different and 25 is the 8th term.

Hence, greatest possible integer in the set = (18 + Range) = (18 + 25) = 43

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GMATGuruNY GMAT Instructor
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Sat Mar 16, 2013 2:53 am
Quote:
A set of 15 different integers has a median of 25 and a range of 25. What is the greatest possible integer that could be in this set?
32
37
40
43
50
Range = biggest - smallest.
Thus:
25 = biggest - smallest.
Smallest = biggest - 25.

We can plug the answer choices into the equation above.
Since we need the greatest possible integer that could be in the set, we should start with the greatest answer choice.

Smallest = 50-25 = 25.
Since all the integers must be different, the smallest integer cannot be equal to the median.
Eliminate E.

Smallest = 43-25 = 18.
Thus, the 7 integers below the median of 25 could be {18,19,20,21,22,23,24}.
The 6 integers between 25 (the median) and 43 (the biggest) could be any 6 different integers between 25 and 43.
This works.

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Sat Mar 16, 2013 2:55 am
[Deleted -- posted in error.]

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Scott@TargetTestPrep GMAT Instructor
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Tue Dec 05, 2017 6:17 pm
paresh_patil wrote:
A set of 15 different integer has a median of 25 & a range of 25. What is the greatest possible integer that could be in this set?
A) 32
B) 37
C) 40
D) 43
E) 50
We are given that there are 15 different integers in a set with a median of 25 and a range of 25. We must determine the greatest possible integer that could be in the set. To determine this integer, we need to first determine the greatest possible value of the least integer from the set.

Since there are 15 total integers in the set, there are 7 integers before the median and 7 integers after the median if we list them in order. We must also keep in mind that each integer is different. Thus, the first 8 integers including the median are the following:

18, 19, 20, 21, 22, 23, 24, 25

Since the range of this set is 25, the greatest number in this set must be 25 more than the smallest integer in the set, and thus the largest number in the set is 18 + 25 = 43.

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