Last visit was: 11 Jul 2025, 08:19 It is currently 11 Jul 2025, 08:19
Close
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

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.
Close
Request Expert Reply
Confirm Cancel
555-605 Level|   Statistics and Sets Problems|                                 
User avatar
EMPOWERgmatRichC
User avatar
Major Poster
Joined: 19 Dec 2014
Last visit: 31 Dec 2023
Posts: 21,788
Own Kudos:
Given Kudos: 450
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Expert
Expert reply
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Posts: 21,788
Kudos: 12,488
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
BLTN
Joined: 25 Aug 2020
Last visit: 19 Dec 2022
Posts: 245
Own Kudos:
Given Kudos: 216
Posts: 245
Kudos: 229
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
GMATinsight
User avatar
Major Poster
Joined: 08 Jul 2010
Last visit: 11 Jul 2025
Posts: 6,378
Own Kudos:
Given Kudos: 128
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
Posts: 6,378
Kudos: 15,578
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
avigutman
Joined: 17 Jul 2019
Last visit: 06 Jul 2025
Posts: 1,294
Own Kudos:
1,888
 [1]
Given Kudos: 66
Location: Canada
GMAT 1: 780 Q51 V45
GMAT 2: 780 Q50 V47
GMAT 3: 770 Q50 V45
Expert
Expert reply
GMAT 3: 770 Q50 V45
Posts: 1,294
Kudos: 1,888
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Video solution from Quant Reasoning:
Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1
User avatar
woohoo921
Joined: 04 Jun 2020
Last visit: 17 Mar 2023
Posts: 519
Own Kudos:
Given Kudos: 623
Posts: 519
Kudos: 118
Kudos
Add Kudos
Bookmarks
Bookmark this Post
BrentGMATPrepNow
Walkabout
If Q is an odd number and the median of Q consecutive integers is 120, what is the largest of these integers?

(A) (Q - 1)/2 + 120
(B) Q/2 + 119
(C) Q/2 + 120
(D) (Q + 119)/2
(E) (Q + 120)/2

A very fast solution is to see what happens when Q = 1.
This means that there's only ONE integer in the set.
So, if the median of the set is 120, then the set is {120}, which means the greatest value in the set is 120

So the correct answer choice should yield 120 when Q = 1.

a) (1-1)/2 + 120 = 120 PERFECT!
b) 1/2 + 119 = some non-integer
c) 1/2 + 120 = some non-integer
d) (1+119)/2 = 60
e) (1+120)/2 = some non-integer

Since only answer choice A yield the correct output, it is the correct answer.

Cheers,
Brent

BrentGMATPrepNow
This is very helpful! How do we know not to test another number (e.g., when Q=3)? Overall, I am confused on the rules pertaining to how to know if you need to test more smart numbers, or do you only need to choose one set of smart numbers if they satisfy all the conditions? Thank you in advance :)
User avatar
BrentGMATPrepNow
User avatar
Major Poster
Joined: 12 Sep 2015
Last visit: 13 May 2024
Posts: 6,755
Own Kudos:
34,057
 [2]
Given Kudos: 799
Location: Canada
Expert
Expert reply
Posts: 6,755
Kudos: 34,057
 [2]
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
woohoo921
BrentGMATPrepNow
This is very helpful! How do we know not to test another number (e.g., when Q=3)? Overall, I am confused on the rules pertaining to how to know if you need to test more smart numbers, or do you only need to choose one set of smart numbers if they satisfy all the conditions? Thank you in advance :)

The key here is that each question on the GMAT has exactly one correct answer.
So, it can't be the case that, when Q = 1, the correct answer is A, but when Q = 3, the correct answer is to something else.
User avatar
Sambon
Joined: 28 Mar 2021
Last visit: 26 Mar 2023
Posts: 23
Own Kudos:
17
 [1]
Given Kudos: 48
Schools: HBS '25 (A)
Products:
Schools: HBS '25 (A)
Posts: 23
Kudos: 17
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Testing cases is the best option here, but here is the algebra for those who are interested:
S = smallest integer, L = largest integer, Q=number of terms in a set (and we're given that it's odd).

In any set of consecutive integers, the mean is equal to the median and either can be found by finding the average of the smallest and the largest integer. Since median is 120, it follows that:
\(\frac{(S+L)}{2} = 120\)
\(S+L = 240\)
\(S = 240-L\)

The number of terms (inclusive) in a set in which the difference between each term is constant is given by:
\(\frac{(L-S)}{(Difference)} + 1\)
Since we have a set of consecutive integers, the difference between each term is 1 and so:

\(Q=(L-S)+1 \)
\(L = Q-1+S \) (Plug in for S using above)
\(L=Q-1+240-L\)
\(2L=Q-1+240\)
\(L=\frac{(Q-1)}{2} + 120\)
User avatar
woohoo921
Joined: 04 Jun 2020
Last visit: 17 Mar 2023
Posts: 519
Own Kudos:
Given Kudos: 623
Posts: 519
Kudos: 118
Kudos
Add Kudos
Bookmarks
Bookmark this Post
BrentGMATPrepNow
woohoo921
BrentGMATPrepNow
This is very helpful! How do we know not to test another number (e.g., when Q=3)? Overall, I am confused on the rules pertaining to how to know if you need to test more smart numbers, or do you only need to choose one set of smart numbers if they satisfy all the conditions? Thank you in advance :)

The key here is that each question on the GMAT has exactly one correct answer.
So, it can't be the case that, when Q = 1, the correct answer is A, but when Q = 3, the correct answer is to something else.




Thank you! To confirm, the only time you would need to choose another smart number or set of smart number(s) to test is when you have more than one answer choice that has the same value? Otherwise, if you get a unique value, you can just move on?
User avatar
EMPOWERgmatRichC
User avatar
Major Poster
Joined: 19 Dec 2014
Last visit: 31 Dec 2023
Posts: 21,788
Own Kudos:
12,488
 [1]
Given Kudos: 450
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Expert
Expert reply
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Posts: 21,788
Kudos: 12,488
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
woohoo921
BrentGMATPrepNow
woohoo921
BrentGMATPrepNow
This is very helpful! How do we know not to test another number (e.g., when Q=3)? Overall, I am confused on the rules pertaining to how to know if you need to test more smart numbers, or do you only need to choose one set of smart numbers if they satisfy all the conditions? Thank you in advance :)

The key here is that each question on the GMAT has exactly one correct answer.
So, it can't be the case that, when Q = 1, the correct answer is A, but when Q = 3, the correct answer is to something else.




Thank you! To confirm, the only time you would need to choose another smart number or set of smart number(s) to test is when you have more than one answer choice that has the same value? Otherwise, if you get a unique value, you can just move on?

Hi woohoo921,

Yes - when TESTing VALUES, if only one of the 5 answers matches what you are looking for, then that answer is the correct answer. If more than one answer matches, then one of those answers is the correct answer (and the other(s) only sometimes match what you are looking for) - meaning that you would then have to TEST again with a different value (or values) to find the one answer that is ALWAYS a match.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at: [email protected]
User avatar
ThatDudeKnows
Joined: 11 May 2022
Last visit: 27 Jun 2024
Posts: 1,070
Own Kudos:
908
 [1]
Given Kudos: 79
Expert
Expert reply
Posts: 1,070
Kudos: 908
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
EMPOWERgmatRichC
woohoo921



Thank you! To confirm, the only time you would need to choose another smart number or set of smart number(s) to test is when you have more than one answer choice that has the same value? Otherwise, if you get a unique value, you can just move on?

Hi woohoo921,

Yes - when TESTing VALUES, if only one of the 5 answers matches what you are looking for, then that answer is the correct answer. If more than one answer matches, then one of those answers is the correct answer (and the other(s) only sometimes match what you are looking for) - meaning that you would then have to TEST only the answer choices that are still remaining (you do not need to test anything that was already eliminated with your first set of values) again with a different value (or values) to find the one answer that is ALWAYS a match.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at: [email protected]

woohoo921

Maybe more cooks in the kitchen than you need, especially since Rich and Brent have already done a great job answering...great enough that I'll simply add a few words to Rich's post (in red) juuuuuust in case it wasn't already clear.
User avatar
sriharsha4444
Joined: 06 Jun 2018
Last visit: 07 Jul 2025
Posts: 39
Own Kudos:
Given Kudos: 760
Posts: 39
Kudos: 17
Kudos
Add Kudos
Bookmarks
Bookmark this Post
If we were to derive it.
nth term in Arithmetic Progression is

\(t_n = a + (n-1)d\)

where a is first term, n is number of the term in the sequence, d is difference between two successive terms and \(t_n\) is the actual value of nth term

120 is the median and Q is given as odd. So it is the \(\frac{(Q+1)}{2}\) th term. Here d is 1 since numbers are consecutive.

\(120 = a + (\frac{(Q+1)}{2} - 1) 1\)

\(120 = a + (\frac{(Q-1)}{2})\)

\(a = 120 - \frac{(Q-1)}{2}\)

We will use this value of a in the next step.

Now the Qth term which will be the largest term in the sequence

\(= a + (Q-1) 1\)

\(= 120 - \frac{(Q-1)}{2} + (Q-1)\)

\(= 120 + \frac{(Q-1)}{2}\)

Ans: A
User avatar
btsaami
Joined: 03 Feb 2023
Last visit: 11 Jul 2025
Posts: 119
Own Kudos:
Given Kudos: 574
Posts: 119
Kudos: 29
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Even if it is confusing at first, we can just check the options by using 1st 5 consecutive no. i.e. 1,2,3,4,5.

3 is the median and the last no. is 5.

Place the value of Q= 5 in options A and D (as B, C and E and already eliminated).

Only A satisfies the condition. Hence, the answer.
User avatar
findingmyself
Joined: 06 Apr 2025
Last visit: 09 Jul 2025
Posts: 88
Own Kudos:
Given Kudos: 37
Posts: 88
Kudos: 11
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Sum of N consecutive integers assuming that we are strating from zero and N=Q

(N(N+1))/2

For an oddly spaced set, mean=median, thus mean =120
120=(Q(Q+1)/2)/Q
Q=239

thus numbers are 1......119(119 numbers) 120 121..........239(119 numbers)
Largest number thus can be expressed as 120+ (Q-1)2

Also you can substitute Q in answer choices which I don't recommend since we need to conceptually solve this problem.

Revert if you have any doubts


Walkabout
If Q is an odd number and the median of Q consecutive integers is 120, what is the largest of these integers?

(A) (Q - 1)/2 + 120
(B) Q/2 + 119
(C) Q/2 + 120
(D) (Q + 119)/2
(E) (Q + 120)/2
   1   2 
Moderators:
Math Expert
102634 posts
PS Forum Moderator
686 posts