Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized for You
we will pick new questions that match your level based on your Timer History
Track Your Progress
every week, we’ll send you an estimated GMAT score based on your performance
Practice Pays
we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
Attend a Veritas Prep GMAT Class for Free. With free trial classes you can work with a 99th percentile expert free of charge. Learn valuable strategies and find your new favorite instructor; click for a list of upcoming dates and teachers.
Are you struggling to achieve your target GMAT score? Most students struggle to cross GMAT 700 because they lack a strategic plan of action. This Free Strategy Webinar, which will empower you to create a well-defined study plan to score 760+ on GMAT.
Re: A set of 15 different integers has median of 25 and a range
[#permalink]
18 Aug 2015, 21:27
21
Expert Reply
21
Bookmarks
Hi All,
When it comes to maximizing or minimizing a value in a group of numbers, you have to think about what the other numbers would need to be to accomplish your goal.
Here, we have a group of 15 DISTINCT (meaning DIFFERENT) integers with a median of 25 and a RANGE of 25. That range will dictate how large the largest value can be.
With a median of 25, we know that 7 numbers are LESS than 25 and 7 numbers are GREATER than 25:
_ _ _ _ _ _ _ 25 _ _ _ _ _ _ _
To maximize the largest value, we need to maximize the smallest value. Here's how we can do it:
18 19 20 21 22 23 24 25 _ _ _ _ _ _ _
With 18 as the smallest value, and a range of 25, the largest value would be 43.
As each integer is different we need to find the maximum values for all those numbers before the median.
the maximum value n7 can have is one less then the median i.e. 24, similarly n6 will be one less than 24 i.e. 23 ... using this process the values for all number before the median would be..
Re: A set of 15 different integers has median of 25 and a range
[#permalink]
12 Aug 2008, 04:16
5
2
Bookmarks
bhushangiri wrote:
A set of 15 different integers has median 25 and range 25. What could be the greatest possible integer in this set ?
OA is 43.
How 43 ? I am getting 50.
50 can not be the highest number.
for the range to be 25, (50 - least number) = 25, i.e least number is 25 But it's given that 25 is median and since each number is different, there must be 7 smaller numbers than 25
Re: A set of 15 different integers has median of 25 and a range
[#permalink]
02 Sep 2013, 13:05
1
1
Bookmarks
bhushangiri wrote:
A set of 15 different integers has median 25 and range 25. What could be the greatest possible integer in this set ?
OA is 43.
How 43 ? I am getting 50.
Try to right down 25 in the middle as a median and 7 numbers to the left and 7 nubers to the right. You will see clearly that the minimum possible least number is 18 to the left of 25. Hence 18+25 -->43
18 19 20 21 22 23 24 25 ....... --> the least possible
Re: A set of 15 different integers has median of 25 and a range
[#permalink]
28 Dec 2015, 06:33
5
The largest in the set minus the smallest in the set should be 25 All the integers are different
Use the options. If 50 is the largest and the range is 25, the smallest is 25, which could have been if the integers were allowed to be same in the set.
Next option to check is 43. 43 - 25 = 18. Can 18 be a part of the set and at the same time there are no repetitions and 25 is the median? Yes
Re: A set of 15 different integers has median of 25 and a range
[#permalink]
28 Dec 2015, 16:47
1
Expert Reply
Hi hdwnkr,
Excellent use of TESTing THE ANSWERS! While that approach isn't nearly as useful overall as TESTing VALUES or the frequent 'math' approaches that will always be an option, it WILL be applicable at least a handful of times on Test Day. Having that approach in your skill-set will help you to quickly (and correctly) solve those few questions and move on with confidence.
Re: A set of 15 different integers has median of 25 and a range
[#permalink]
29 Dec 2015, 12:49
2
EMPOWERgmatRichC wrote:
Hi hdwnkr,
Excellent use of TESTing THE ANSWERS! While that approach isn't nearly as useful overall as TESTing VALUES or the frequent 'math' approaches that will always be an option, it WILL be applicable at least a handful of times on Test Day. Having that approach in your skill-set will help you to quickly (and correctly) solve those few questions and move on with confidence.
GMAT assassins aren't born, they're made, Rich
Thanks a lot for the encouragement. Much appreciated! Helps when I am just days away from the D Day _________________
As each integer is different we need to find the maximum values for all those numbers before the median.
the maximum value n7 can have is one less then the median i.e. 24, similarly n6 will be one less than 24 i.e. 23 ... using this process the values for all number before the median would be..
Re: A set of 15 different integers has median of 25 and a range
[#permalink]
27 Oct 2016, 16:13
Expert Reply
bhushangiri wrote:
A set of 15 different integers has median of 25 and a range of 25. What is 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.
Re: A set of 15 different integers has median of 25 and a range
[#permalink]
27 Oct 2016, 17:37
Expert Reply
Hi Mitty,
Since the question asks for the LARGEST POSSIBLE integer that could be in the set of numbers, we have to tailor our work around a certain 'math idea' - since we have a range of 25, to get the largest possible integer, we need the smallest integer in the set to be as big as possible. Working 'backwards' from the median - and keeping in mind that all of the values are distinct - the numbers BELOW the median would have to be consecutive. In that way, we could make the smallest number as big as possible.
Re: Set of 15 different integers
[#permalink]
10 Nov 2016, 20:16
3
Top Contributor
Expert Reply
spc11 wrote:
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? 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)
Re: A set of 15 different integers has median of 25 and a range
[#permalink]
11 Nov 2016, 00:08
2
Expert Reply
bhushangiri wrote:
A set of 15 different integers has median of 25 and a range of 25. What is greatest possible integer that could be in this set?
A. 32 B. 37 C. 40 D. 43 E. 50
The constraints are median (which is easy to handle - just that the 8th integer will be 25) and range (which is 25). The important thing is that all integers are different. For the range to be constant and then have the greatest possible integer, the smallest integer should be as large as possible.
Since all integers are distinct, the smallest integer should be 7 less than 25 i.e. 18 (so 18, 19, 20, 21, 22, 23, 24, 25 are the first 8 integers)
For the range to be 25, the greatest integer should be 18+25 = 43
Answer (D) _________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Re: A set of 15 different integers has median of 25 and a range
[#permalink]
25 Nov 2017, 01:17
matthewsmith_89 wrote:
I think the easiest way to approach this problem is process elimination Let's look at answer D which is 43 25 is the 8th number in the sequence
43 - x = 25 x = 43 - 25 x = 18
18, 19, 20, 21, 22, 23, 24, 25
Therefore, the answer is D
Hi,
I have a question here, it is mentioned that the median is 25 or we can say the 8th element is 25 and the range is 25 but it's nowhere mentioned that the numbers are consecutive. Then how did you assume them to be consecutive integers?
If I take 37 as the greatest number, then the first element must be 12 and it can still satisfy 12,15,17,19,21,23,24,25
25 can be the median in this case too..or is it a strict rule to assume the numbers in consecutive order? Please explain
As per my knowledge, for the range to be constant, and to find the greatest integer, the smallest integer must be as large as possible.. Here 18 can be the largest..so we have to take 43..
Re: A set of 15 different integers has median of 25 and a range
[#permalink]
25 Nov 2017, 14:22
1
Expert Reply
Hi Pratyaksh2791,
This question asks us to find the greatest possible number that could be in this set. Since 25 is the MEDIAN of the group of 15 INTEGERS, we know that 7 integers are greater than 25 and 7 integers are less than 25. We're told that the largest integer is exactly 25 more than the smallest integer, so to maximize the biggest value, we also have to maximize the smallest value. Since we're restricted to INTEGERS, the only way to get that maximum result is if the 7 integers that are less than 25 are CONSECUTIVE integers:
Re: A set of 15 different integers has median of 25 and a range
[#permalink]
19 Jan 2018, 14:39
So does that mean that this set does not contain any -ve integers? I am assuming it can not but why? _________________
1. Well Begun is Half done 2. He who asks a question is a fool for five minutes; he who does not ask a question remains a fool forever. 3. The night is darkest just before the dawn
Re: A set of 15 different integers has median of 25 and a range
[#permalink]
19 Jan 2018, 19:22
Expert Reply
Hi Rocket7,
The question tells us that the RANGE of the numbers is 25... and asks us to find the largest POSSIBLE integer that could be in the set. If you look at the five answer choices - and then subtract 25 from each, you'll see that the SMALLEST number that would correspond to each of those answers would be a positive integer. Thus, the set CANNOT contain any negative numbers.