Last visit was: 18 Jul 2025, 15:24 It is currently 18 Jul 2025, 15:24
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
BillyZ
User avatar
Current Student
Joined: 14 Nov 2016
Last visit: 03 May 2025
Posts: 1,147
Own Kudos:
21,935
 [34]
Given Kudos: 926
Location: Malaysia
Concentration: General Management, Strategy
Schools: Sloan '23 (D) Tuck '23 (D) Darden '23 (D) Ross '23 (D) Kellogg '23 (D) Wharton '23 (D) Booth '23 (D) Fuqua '24 (A) Harvard '24 (D) Stanford '24 (D)
GMAT 1: 750 Q51 V40 (Online)
GPA: 3.53
Products:
My Reviews
Schools: Sloan '23 (D) Tuck '23 (D) Darden '23 (D) Ross '23 (D) Kellogg '23 (D) Wharton '23 (D) Booth '23 (D) Fuqua '24 (A) Harvard '24 (D) Stanford '24 (D)
GMAT 1: 750 Q51 V40 (Online)
Posts: 1,147
Kudos: 21,935
 [34]
Set X of has an average of 61. If the largest element is 7 greater tha 29 Jan 2017, 05:50
3
Kudos
Add Kudos
31
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
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:

31% (02:42) correct 69% (02:39) wrong based on 207 sessions

History

Date
Time
Result
Not Attempted Yet
Set \(X\) of has an average of \(61\). If the largest element is 7 greater than 6 times the smallest element, how many values out of \({2,3,5,8,9,11,53,102,123,178,210,267,283,311,376,383,399,401}\) can be a part of Set \(X\)?

(A) 18
(B) 13
(C) 9
(D) 7
(E) cannot be determined
ShowHide Answer
Official Answer
C
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 18 Jul 2025
Posts: 11,294
Own Kudos:
41,823
 [1]
Given Kudos: 333
Status:Math and DI Expert
Products:
My Reviews
Expert
Expert reply
Posts: 11,294
Kudos: 41,823
 [1]
Set X of has an average of 61. If the largest element is 7 greater tha 29 Jan 2017, 08:53
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
ziyuenlau
Set \(X\) of has an average of \(61\). If the largest element is 7 greater than 6 times the smallest element, how many values out of \({2,3,5,8,9,11,53,102,123,178,210,267,283,311,376,383,399,401}\) can be a part of Set \(X\)?

(A) 18
(B) 13
(C) 9
(D) 7
(E) cannot be determined

I think this Q has already been discussed earlier. I hope you have searched for it before posting.
Average is 61..find the max and min values possible, you will get the answer
avatar
LHC8717
avatar
Joined: 25 Nov 2016
Last visit: 29 Aug 2017
Posts: 43
Own Kudos:
26
 [1]
Given Kudos: 12
Location: Switzerland
GPA: 3
Posts: 43
Kudos: 26
 [1]
Set X of has an average of 61. If the largest element is 7 greater tha 29 Jan 2017, 10:17
Kudos
Add Kudos
Bookmarks
Bookmark this Post
The average is 61 therefore the max value must be higher

We know that the largest value is 6 times the smallest plus 7

=> (61-7)/6 = 9 => The smallest value must be grater than 9

The max value will be 61*6 + 7 = 373 => The largest value must be less than 373

=> The number in the set must be 9<X<373 => 9 values
User avatar
annusngh
User avatar
Joined: 30 Jul 2013
Last visit: 24 Aug 2018
Posts: 16
Own Kudos:
58
Given Kudos: 54
Location: India
Concentration: International Business, Strategy
GPA: 2.4
WE:General Management (Insurance)
Posts: 16
Kudos: 58
Set X of has an average of 61. If the largest element is 7 greater tha 29 Jan 2017, 11:38
Kudos
Add Kudos
Bookmarks
Bookmark this Post
LHC8717
The average is 61 therefore the max value must be higher

We know that the largest value is 6 times the smallest plus 7

=> (61-7)/6 = 9 => The smallest value must be grater than 9

The max value will be 61*6 + 7 = 373 => The largest value must be less than 373

=> The number in the set must be 9<X<373 => 9 values


Hi,
Let's say smallest is X then,
{X+(6X+7)}/2 = 61

7X = 122 - 7

X = 115/7

Now, pls suggest what am I doing wrong?

Thanks,
avatar
AlexGmat2017
avatar
Joined: 13 Jan 2017
Last visit: 20 Apr 2021
Posts: 31
Own Kudos:
5
Given Kudos: 92
Posts: 31
Kudos: 5
Set X of has an average of 61. If the largest element is 7 greater tha 29 Jan 2017, 13:32
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Answer (C) is right.

2,3,5,8, can not be a part of X. Even if one of them is a min element of X then the max element is not greater 61 and the average of X cannot be 61.
376,383,399,401 can not be a part of X. Even if one of them is a max element of X then the min element is not less than 61 and the average of X cannot be 61.
User avatar
stonecold
User avatar
Joined: 12 Aug 2015
Last visit: 09 Apr 2024
Posts: 2,248
Own Kudos:
3,471
 [4]
Given Kudos: 893
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Posts: 2,248
Kudos: 3,471
 [4]
Set X of has an average of 61. If the largest element is 7 greater tha 05 Aug 2017, 22:54
2
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
Here is what I did for this one-->

Smallest value = a(let)
Largest value => 6a+7


Now the smallest value of the set must be less than the mean and the largest value must be greater than the mean.

Hence a>61
and 6a+7>61 ==> a>9

At a=61 => Largest value => 6a+7= 373

Hence the range of the set would be (9,373)

Only 9 elements are in the range.

Hence C.

NOTE --> THIS QUESTION is a part of the MOCK SERIES --> https://gmatclub.com/forum/stonecold-s- ... l#p1676182
User avatar
goforgmat
User avatar
Joined: 09 Feb 2015
Last visit: 02 Nov 2019
Posts: 246
Own Kudos:
106
Given Kudos: 232
Location: India
Concentration: Social Entrepreneurship, General Management
Schools: Booth '21 (D) Cambridge "21 (D) LBS '22 (D)
GMAT 1: 690 Q49 V34
GMAT 2: 720 Q49 V39
GPA: 2.8
Products:
My Reviews
Schools: Booth '21 (D) Cambridge "21 (D) LBS '22 (D)
GMAT 2: 720 Q49 V39
Posts: 246
Kudos: 106
Set X of has an average of 61. If the largest element is 7 greater tha 10 Aug 2017, 10:44
Kudos
Add Kudos
Bookmarks
Bookmark this Post
annusngh
LHC8717
The average is 61 therefore the max value must be higher

We know that the largest value is 6 times the smallest plus 7

=> (61-7)/6 = 9 => The smallest value must be grater than 9

The max value will be 61*6 + 7 = 373 => The largest value must be less than 373

=> The number in the set must be 9<X<373 => 9 values


Hi,
Let's say smallest is X then,
{X+(6X+7)}/2 = 61

7X = 122 - 7

X = 115/7

Now, pls suggest what am I doing wrong?

Thanks,

You are assuming the numbers in the set to be in AP. Its not given in the problem!
User avatar
hellosanthosh2k2
User avatar
Joined: 02 Apr 2014
Last visit: 07 Dec 2020
Posts: 362
Own Kudos:
565
 [1]
Given Kudos: 1,227
Location: India
Schools: XLRI"20
GMAT 1: 700 Q50 V34
GPA: 3.5
Schools: XLRI"20
GMAT 1: 700 Q50 V34
Posts: 362
Kudos: 565
 [1]
Set X of has an average of 61. If the largest element is 7 greater tha Updated on: 15 May 2018, 21:31
Originally posted by hellosanthosh2k2 on 03 Jan 2018, 01:42.
Last edited by hellosanthosh2k2 on 15 May 2018, 21:31, edited 1 time in total.
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Given average \(61\) and \(max\) = \(min * 6 + 7\), so set must have alteast two different integers (meaning it is not a set of all same integers)

in a set of different integers, min value can't be equal to average, so \(min\) < \(61\) => \(max\) < \(61 * 6 + 7\), so \(max\) < \(373\)
similarly, max value can't be equal to average, so \(max\) > \(61\) => \(61\) < \(max\) < \(373\)

now we found, \(max\) > \(61\)=> \(min * 6 + 7\) > \(61\) => \(min\) > \(9\).

all the elements in the set must be between \(9 < S < 373\), only 9 integers of the given falls within the range => Answer (C)
User avatar
SAHILJPR
User avatar
Joined: 04 Feb 2017
Last visit: 27 Aug 2021
Posts: 6
Own Kudos:
6
Given Kudos: 43
Location: India
Concentration: Marketing, Human Resources
WE:Sales (Manufacturing)
Posts: 6
Kudos: 6
Set X of has an average of 61. If the largest element is 7 greater tha 10 Jan 2018, 19:12
Kudos
Add Kudos
Bookmarks
Bookmark this Post
stonecold
Here is what I did for this one-->

Smallest value = a(let)
Largest value => 6a+7


Now the smallest value of the set must be less than the mean and the largest value must be greater than the mean.

Hence a>61
and 6a+7>61 ==> a>9

At a=61 => Largest value => 6a+7= 373

Hence the range of the set would be (9,373)




Only 9 elements are in the range.

Hence C.

NOTE --> THIS QUESTION is a part of the MOCK SERIES --> https://gmatclub.com/forum/stonecold-s- ... l#p1676182


I'm confused how you derived the largest value 373 by taking a=61.

Can you please explain.
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 37,454
Own Kudos:
1,013
Posts: 37,454
Kudos: 1,013
Set X of has an average of 61. If the largest element is 7 greater tha 29 Apr 2024, 17:49
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
102619 posts
Krunaal
PS Forum Moderator
698 posts