Last visit was: 19 Nov 2025, 07:57 It is currently 19 Nov 2025, 07:57
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,389
Own Kudos:
778,259
 [12]
Given Kudos: 99,977
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,389
Kudos: 778,259
 [12]
The average (arithmetic mean) of 17 consecutive integers is an odd num 15 Nov 2019, 01:47
Kudos
Add Kudos
12
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

45% (medium)

Question Stats:

65% (01:59) correct 35% (02:05) wrong based on 371 sessions

History

Date
Time
Result
Not Attempted Yet
The average (arithmetic mean) of 17 consecutive integers is an odd number. Which of the following must be true?

I. Largest integer is even.
II. Sum of all integers is odd.
III. Difference between largest and smallest integer is even.

(A) I only
(B) II only
(C) III only
(D) I and II only
(E) II and III only


Are You Up For the Challenge: 700 Level Questions
ShowHide Answer
Official Answer
E
User avatar
EgmatQuantExpert
User avatar
e-GMAT Representative
Joined: 04 Jan 2015
Last visit: 02 Apr 2024
Posts: 3,663
Own Kudos:
20,165
 [3]
Given Kudos: 165
Expert
Expert reply
Posts: 3,663
Kudos: 20,165
 [3]
The average (arithmetic mean) of 17 consecutive integers is an odd num 15 Nov 2019, 04:10
2
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post

Solution



Given
    • Average (arithmetic mean) of 17 consecutive integers is an odd number

To find
    • Correct statements

Approach and Working out

Let the consecutive integers are a, a+1, a+2, a+3, ……., a+16.
    • Sum of all the integers = 17a + (1+2+3+ .. +16) = 17a + 16*17/2 = 17a + 8*17= 17(a+8)
      o Average = 17(a + 8)/17 = a + 8 =odd
         So, a = Odd
         Thus, first term is odd.

Statement 1:
    • a + 16 = odd + even = odd
    • Not true
.

Statement 2:
    • Sum = 17(a+8) = odd × odd = odd
    • True

Statement 3:
    • Largest integer – Smallest integer = a+ 16 – a = 16= Even
    • True

Thus, option E is the correct answer.
Correct Answer: Option E
User avatar
exc4libur
User avatar
Joined: 24 Nov 2016
Last visit: 22 Mar 2022
Posts: 1,684
Own Kudos:
1,447
Given Kudos: 607
Location: United States
Posts: 1,684
Kudos: 1,447
The average (arithmetic mean) of 17 consecutive integers is an odd num 19 Nov 2019, 04:49
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
The average (arithmetic mean) of 17 consecutive integers is an odd number. Which of the following must be true?

I. Largest integer is even.
II. Sum of all integers is odd.
III. Difference between largest and smallest integer is even.

(A) I only
(B) II only
(C) III only
(D) I and II only
(E) II and III only
Show more

{1,2,3,4,5}: mean = 3 (odd); rng=5-1=4 (even); sum=3*5=15 (odd)
{2,3,4,5,6}: mean = 4 (even); rng=6-2=4 (even); sum=4*5=20 (even)

Ans (E)
User avatar
Abhishek009
User avatar
Board of Directors
Joined: 11 Jun 2011
Last visit: 18 Jul 2025
Posts: 5,934
Own Kudos:
5,327
Given Kudos: 463
Status:QA & VA Forum Moderator
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Posts: 5,934
Kudos: 5,327
The average (arithmetic mean) of 17 consecutive integers is an odd num 19 Nov 2019, 11:32
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
The average (arithmetic mean) of 17 consecutive integers is an odd number. Which of the following must be true?

I. Largest integer is even.
II. Sum of all integers is odd.
III. Difference between largest and smallest integer is even.

(A) I only
(B) II only
(C) III only
(D) I and II only
(E) II and III only


Are You Up For the Challenge: 700 Level Questions
Show more
Sum of first n numbers is \(1+ 2+ ... + n = \frac{n(n+1) }{ 2}\)

Now, sum of first 17 numbers will be \(\frac{17*18}{2} = 153\) and its average will be \(\frac{153}{17} = 9\) (Odd)

1. Largest number is Odd (17)
2. Sum of all integers is Odd (153)
3. Difference between largest and smallest integer is even. ( 17 - 1 = 16)

Hence, only (E) holds true, Answer must be (E)
User avatar
satya2029
User avatar
Joined: 10 Dec 2017
Last visit: 29 Sep 2025
Posts: 231
Own Kudos:
249
 [1]
Given Kudos: 138
Location: India
Posts: 231
Kudos: 249
 [1]
The average (arithmetic mean) of 17 consecutive integers is an odd num 22 Nov 2019, 07:20
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
The average (arithmetic mean) of 17 consecutive integers is an odd number. Which of the following must be true?

I. Largest integer is even.
II. Sum of all integers is odd.
III. Difference between largest and smallest integer is even.

(A) I only
(B) II only
(C) III only
(D) I and II only
(E) II and III only


Are You Up For the Challenge: 700 Level Questions
Show more
a9 is odd
For this a1 is odd and a17 is odd
so largest integer is odd
For consecutive integers
Sum of the terms= AM*no. of terms
and AM= (First +Last)/2=odd (given)
Sum of the terms= odd* odd=odd
a1 is odd and a17 is odd
Difference=a17-a1= Even
E:)
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 18 Nov 2025
Posts: 21,712
Own Kudos:
26,995
Given Kudos: 300
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 21,712
Kudos: 26,995
The average (arithmetic mean) of 17 consecutive integers is an odd num 23 Jan 2020, 11:44
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
The average (arithmetic mean) of 17 consecutive integers is an odd number. Which of the following must be true?

I. Largest integer is even.
II. Sum of all integers is odd.
III. Difference between largest and smallest integer is even.

(A) I only
(B) II only
(C) III only
(D) I and II only
(E) II and III only


Are You Up For the Challenge: 700 Level Questions
Show more

Since the mean (or average) of a set of consecutive integers is equal to the median, we see that the median is also odd. Now let’s analyze the Roman numeral statements.

I. Largest integer is even.

The largest number in terms of the median (or the middle number) is (17 - 1)/2 = 8 more than the median. Since the median is odd and odd + 8 = odd + even = odd, we see that the largest number is odd also. Statement I is not ture.

II. Sum of all integers is odd.

Since sum = average x quantity and here we have average = odd and quantity = 17, we see that Sum = odd x 17 = odd x odd = odd. Statement II is true.

III. Difference between the largest and smallest integers is even.

In I, we see that the largest number is 8 more than the median, i.e., largest number = median + 8. Therefore, the smallest number should be 8 less than the median, i.e., smallest number = median - 8. So we have:

largest number - smallest number = (median + 8) - (median - 8) = 8 + 8 = 16

Statement III is true.

Answer: E
User avatar
sujoykrdatta
User avatar
Joined: 26 Jun 2014
Last visit: 19 Nov 2025
Posts: 547
Own Kudos:
1,114
Given Kudos: 13
Status:Mentor & Coach | GMAT Q51 | CAT 99.98
GMAT 1: 750 Q51 V39
Expert
Expert reply
GMAT 1: 750 Q51 V39
Posts: 547
Kudos: 1,114
The average (arithmetic mean) of 17 consecutive integers is an odd num 23 Jan 2020, 13:16
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Question:
The average (arithmetic mean) of 17 consecutive integers is an odd number. Which of the following must be true?
I. Largest integer is even.
II. Sum of all integers is odd.
III. Difference between largest and smallest integer is even.
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) II and III only


Solution:
We know that: The average (arithmetic mean) of 17 consecutive integers is an odd number.

Consecutive integers refer to integers having a common difference of 1, for example: 11, 12, 13, 14, ..
In such a scenario, the arithmetic mean (average) is always equal to the median
[In short: in an arithmetic progression: mean equals the median]

Thus, for 17 integers, the median is the \([(17+1)/2] th\) term i.e. the 9th term
Since the above median (or mean) is an odd number, we have:

The 9th number is odd (hence: 8th is even, 7th is odd ... and the 1st number is odd)
Similarly, the 17th term is 8 more than the 9th term i.e. 8 more than an odd number; hence is odd

Let us look at the statements:
I) The largest number is the 17th term, which is odd
II) Sum of all numbers = 17 x (Mean) = 17 x (odd number), which is odd
III) Difference between the largest and smallest numbers = Odd - Odd = Even

Thus, statements II and III are correct

Answer E
User avatar
KarishmaB
User avatar
Joined: 16 Oct 2010
Last visit: 18 Nov 2025
Posts: 16,267
Own Kudos:
76,994
Given Kudos: 482
Location: Pune, India
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 16,267
Kudos: 76,994
The average (arithmetic mean) of 17 consecutive integers is an odd num 23 Jan 2020, 20:37
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
The average (arithmetic mean) of 17 consecutive integers is an odd number. Which of the following must be true?

I. Largest integer is even.
II. Sum of all integers is odd.
III. Difference between largest and smallest integer is even.

(A) I only
(B) II only
(C) III only
(D) I and II only
(E) II and III only


Are You Up For the Challenge: 700 Level Questions
Show more


The average (arithmetic mean) of 17 consecutive integers is an odd number - This means the middle number (9th) is odd.
So the 17 numbers are made up of 8 numbers before and after the middle number. e.g. if the middle number (average) is 9, the numbers would be 1 to 17 - 1 to 8 before 9 and 10 to 17 after 9.

I. Largest integer is even.
Largest integer here is 17. Not even.

II. Sum of all integers is odd.
We have 8 even integers and 9 odd integers. Since we have an odd number of odd integers, the sum will be odd.

III. Difference between largest and smallest integer is even.
Smallest and the largest integers both will be odd. So their difference will be even.

Answer (E)
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,588
Own Kudos:
1,079
Posts: 38,588
Kudos: 1,079
The average (arithmetic mean) of 17 consecutive integers is an odd num 20 Apr 2025, 20:22
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Moderators:
Bunuel
Math Expert
105389 posts
Krunaal
Tuck School Moderator
805 posts