by: Bunuel
3 mins
Events & Promotions
|
|
GMAT Club Daily Prep
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Sep 1312:30 AM EDT
-01:30 AM EDT
Struggling to find the right strategies to score a 99 %ile on GMAT Focus? Riya (GMAT 715) boosted her score by 100-points in just 15 days! Discover how the right mentorship, tailored strategies, and an unwavering mindset can transform your GMAT prep.
Sep 1301:30 AM EDT
-02:30 AM EDT
At one point, she believed GMAT wasn’t for her. After scoring 595, self-doubt crept in and she questioned her potential. But instead of quitting, she made the right strategic changes. The result? A remarkable comeback to 695. Check out how Saakshi did it.
Sep 1507:00 PM EDT
-09:00 PM EST
Elite scores are possible when you enroll in a powerful GMAT course, taught live online + 6 months access to TTP OnDemand video courses included! Class starts Tues/Thurs Sept. 15, 2026 - Nov. 15, 2027, 7:00pm-9:00pm EST
Sep 2107:00 PM EDT
-10:00 PM EDT
Boost your GMAT score in less than one month in a live online class + 6 months access to TTP OnDemand video courses included! Class starts Mon, Tues, Wed, Thur, Fri Sept. 21, 2026 - Oct. 9, 2027, 7:00pm-10:00pm EST
Posts: 83
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
48% (02:32) correct
52%
(02:48)
wrong
based on 162
sessions
History
Date
Time
Result
Not Attempted Yet
There are five distinct positive integers such that their median is 9 and mean is 8. If the average of 2nd smallest and 2nd largest number is 8 then find the range of these five integers.
A. 24
B. 22
C. 15
D. 13
E. 10
A. 24
B. 22
C. 15
D. 13
E. 10
Posts: 83
Let the numbers are a, b, 9, d, e.
According to the question: (a+b+9+d+e)/5 = 8
a + b + 9 + d + e = 40 or a+b+d+e= 31......(1)
According to the question: (b + d) / 2 = 8 or b+d= 16....(2)
Equation (1) equation (2) gives: a + e = 15
To maximize the range we need to maximize the difference between e and a and we can do so by maximize the value of e and minimize the value of a.
As the numbers are positive integers, so the minimum possible value of a = 1 and maximum possible value of e = 15 - 1 = 14 Maximum possible range= e-a = 14-1=13.
According to the question: (a+b+9+d+e)/5 = 8
a + b + 9 + d + e = 40 or a+b+d+e= 31......(1)
According to the question: (b + d) / 2 = 8 or b+d= 16....(2)
Equation (1) equation (2) gives: a + e = 15
To maximize the range we need to maximize the difference between e and a and we can do so by maximize the value of e and minimize the value of a.
As the numbers are positive integers, so the minimum possible value of a = 1 and maximum possible value of e = 15 - 1 = 14 Maximum possible range= e-a = 14-1=13.
GraemeGmatPanda
Joined: 13 Apr 2020
Last visit: 08 Sep 2026
Posts: 102
Location: United Kingdom
Concentration: Marketing
Schools: LBS '16 (A$)
Products:
Schools: LBS '16 (A$)
Posts: 102
List the five integers in increasing order and identify the median.
\(a < b < 9 < d < e\)
Express the sum of the five integers using the mean of 8.
\(a + b + 9 + d + e = 5 \times 8\)
Simplify the sum equation.
\(a + b + 9 + d + e = 40\)
Use the given average of the second smallest and second largest integers.
\(\frac{b + d}{2} = 8\)
Simplify to express \(b + d\).
\(b + d = 16\)
Isolate the sum of the smallest and largest integers by removing the median from the total.
\(a + b + d + e = 40 - 9\)
Simplify this expression.
\(a + b + d + e = 31\)
Substitute \(b + d = 16\) to find \(a + e\).
\(a + e = 31 - (b + d) = 31 - 16\)
Simplify to get the sum of the smallest and largest.
\(a + e = 15\)
Determine the smallest integer under the ordering constraints (ensuring \(d>9\) when \(b+d=16\)).
\(a = 1\)
Find the largest integer using \(a+e=15\).
\(e = 15 - 1 = 14\)
Compute the range as the difference between the largest and smallest integers.
\(\text{Range} = e - a = 14 - 1\)
Finalize the numerical value of the range.
\(\text{Range} = 13\)
Answer 13, since the only valid set of numbers yields smallest integer 1 and largest integer 14, giving range 14 − 1 = 13.
ʕ•ᴥ•ʔ
_________________
\(a < b < 9 < d < e\)
Express the sum of the five integers using the mean of 8.
\(a + b + 9 + d + e = 5 \times 8\)
Simplify the sum equation.
\(a + b + 9 + d + e = 40\)
Use the given average of the second smallest and second largest integers.
\(\frac{b + d}{2} = 8\)
Simplify to express \(b + d\).
\(b + d = 16\)
Isolate the sum of the smallest and largest integers by removing the median from the total.
\(a + b + d + e = 40 - 9\)
Simplify this expression.
\(a + b + d + e = 31\)
Substitute \(b + d = 16\) to find \(a + e\).
\(a + e = 31 - (b + d) = 31 - 16\)
Simplify to get the sum of the smallest and largest.
\(a + e = 15\)
Determine the smallest integer under the ordering constraints (ensuring \(d>9\) when \(b+d=16\)).
\(a = 1\)
Find the largest integer using \(a+e=15\).
\(e = 15 - 1 = 14\)
Compute the range as the difference between the largest and smallest integers.
\(\text{Range} = e - a = 14 - 1\)
Finalize the numerical value of the range.
\(\text{Range} = 13\)
Answer 13, since the only valid set of numbers yields smallest integer 1 and largest integer 14, giving range 14 − 1 = 13.
ʕ•ᴥ•ʔ
_________________
Graeme
Coach & Founder of GMAT Panda
Coach & Founder of GMAT Panda
Since the sum of the smallest and largest equals 15 for the reasons others describe, the range can't be >15, so the given answer is incorrect.
Additionally, since therefore the smallest is 15-largest, the range is:
Largest - (15-largest) =
2*largest - 15 = odd number.
The only answer choice that fits is 13
Additionally, since therefore the smallest is 15-largest, the range is:
Largest - (15-largest) =
2*largest - 15 = odd number.
The only answer choice that fits is 13
Posts: 124
Let's assume the five distinct positive integers in increasing order be
a<b<9<d<e
Given conditions
Median = 9
Mean = 8
total sum = 5×8 = 40.
Average of 2nd smallest and 2nd largest is 8
(b+d)/2=8
⇒b+d=16
Use the sum
a+b+9+d+e=40
Substitute - b+d=16:
a+e+16+9=40
⇒a+e=15
Apply ordering constraints
b<9<d and b+d=16
This gives valid pairs:
(b,d)=(6,10),(5,11),(4,12),(3,13)
For each case,
a<b and e>d with a+e=15
Checking all valid combinations yields the following possible ranges:
e−a∈{7,9,11,13}
a<b<9<d<e
Given conditions
Median = 9
Mean = 8
total sum = 5×8 = 40.
Average of 2nd smallest and 2nd largest is 8
(b+d)/2=8
⇒b+d=16
Use the sum
a+b+9+d+e=40
Substitute - b+d=16:
a+e+16+9=40
⇒a+e=15
Apply ordering constraints
b<9<d and b+d=16
This gives valid pairs:
(b,d)=(6,10),(5,11),(4,12),(3,13)
For each case,
a<b and e>d with a+e=15
Checking all valid combinations yields the following possible ranges:
e−a∈{7,9,11,13}
Bunuel, can you kindly once check this question and help with a solution?
Out of the options mentioned, only 13 seem feasible. I am not sure what is happening here.
Out of the options mentioned, only 13 seem feasible. I am not sure what is happening here.
shriwasakshat
gchandana
Yes, the OA is 13. Fixed the options.
_________________
New to the GMAT Club?
- • Questions: Question Bank | Bunuel's Signature Collection
• Tests: GMAT Club Tests | Forum Quiz
• Guides: Quantitative | Critical Reasoning | Reading Comprehension | Ultimate Quant Guide | All You Need for Quant
• Rules: Quantitative | Verbal
Posts: 25
I won't post my whole solution, but there are a few tricks that made this (eventually) work for me. I didn't need to use max/min logic or test a bunch of ordered pairs.
One, recognize that you can find the sum of a set by multiplying Mean*Count, even if (as in this case) the set is skewed.
Two, after some plug n' chug work, you come to the equation: a + e = 15. What we need is, of course, e-a, the range.
Just subtract 2a from both sides, and you get e - a = 15-2a, which we know from the prompt must be an integer, and 2*a must also be an integer, and the range must necessarily be less than 15!
That only leaves two answer options: 10 or 13. A little backsolvong makes it clear: If the range = 10, then 2*a =5, and there is no integer solution to that equation!
So range = 13 it is.
One, recognize that you can find the sum of a set by multiplying Mean*Count, even if (as in this case) the set is skewed.
Two, after some plug n' chug work, you come to the equation: a + e = 15. What we need is, of course, e-a, the range.
Just subtract 2a from both sides, and you get e - a = 15-2a, which we know from the prompt must be an integer, and 2*a must also be an integer, and the range must necessarily be less than 15!
That only leaves two answer options: 10 or 13. A little backsolvong makes it clear: If the range = 10, then 2*a =5, and there is no integer solution to that equation!
So range = 13 it is.
The question is NOT what is the maximum possible range. It is "what is the range?"
There are four possible answers for that: 7,9,11,13.
13 is the only one that is in the selections.
However, the question should be changed.
Either to "What is the maximum possible range?" or to ¿Which of the following answers could be the range?"
_________________
There are four possible answers for that: 7,9,11,13.
13 is the only one that is in the selections.
However, the question should be changed.
Either to "What is the maximum possible range?" or to ¿Which of the following answers could be the range?"
_________________
Clipper Ledgard
GMAT Coach
GMAT Coach
Moderator:
Announcements
How to Tell If Your GMAT Prep Resources Are Actually Helping You
Subscribe to GMAT Club for New Podcast Episodes, Debriefs, & Insightful Sessions on GMAT Preparation
Subscribe to GMAT Club for New Podcast Episodes, Debriefs, & Insightful Sessions on GMAT Preparation
Tuck at Dartmouth
AI at Dartmouth Tuck: How the School Is Preparing Leaders for the Age of Artificial Intelligence
Inside the courses, research, and hands-on learning defining wise, decisive leadership in an AI-driven world.
Read More
Inside the courses, research, and hands-on learning defining wise, decisive leadership in an AI-driven world.
Read More
Top 5 GMAT Debrief Videos
Success stories and strategies from high-scoring candidates.