by: Bunuel
11 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 1008:00 PM PDT
-09:00 PM PDT
Free- full-length test + 15 concept videos + 150+ short videos + study plan!
Sep 0812:30 AM EDT
-01:30 AM EDT
Looking for your GMAT motivation to break through the score plateau? Pragati improved her score by massive 160 points with strategic guidance and hard-work! Find out how personalized mentorship and a strong mindset can turn GMAT struggles into success.
Sep 1001:00 AM EDT
-02:00 AM EDT
Learn how Keshav, a Chartered Accountant, scored an impressive 705 on GMAT in just 30 days with GMATWhiz's expert guidance. In this video, he shares preparation tips and strategies that worked for him, including the mock, time management, and more.
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
GMAT 1: 760 Q51 V42
Posts: 10,057
Updated on: 19 Jul 2024, 07:42
Originally posted by MathRevolution on 01 Sep 2019, 21:59.
Last edited by Bunuel on 19 Jul 2024, 07:42, edited 2 times in total.
Last edited by Bunuel on 19 Jul 2024, 07:42, edited 2 times in total.
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
53% (02:21) correct
47%
(02:44)
wrong
based on 213
sessions
History
Date
Time
Result
Not Attempted Yet
\(A=\{1, 2, 3, 4, 5\}\) is given. If there are \(1,2,…,n\) subsets of \(A\), let A1, A2 , A3 ,… , An be the sums of the elements of the corresponding subsets of \(A\). What is A1+ A2,+ A3+… + An?
\(A. 200\)
\(B. 210\)
\(C. 230\)
\(D. 240\)
\(E. 250\)
\(A. 200\)
\(B. 210\)
\(C. 230\)
\(D. 240\)
\(E. 250\)
GMAT 1: 760 Q51 V42
Posts: 10,057
tgubbay1
The subsets of \(A = \{1,2,3,4,5\}\) are as follows.
\(S_1 = \{\}\),
\(S_2 = \{1\}\),
\(S_3 = \{2\}\),
\(S_4 = \{3\}\),
\(S_5 = \{4\}\),
\(S_6 = \{5\}\),
\(S_7 = \{1,2\}\),
\(S_8 = \{1,3\}\),
\(S_9 = \{1,4\}\),
\(S_{10} = \{1,5\}\),
\(S_{11} = \{2,3\}\),
\(S_{12} = \{2,4\}\),
\(S_{13} = \{2,5\}\),
\(S_{14} = \{3,4\}\),
\(S_{15} = \{3,5\}\),
\(S_{16} = \{4,5\}\),
\(S_{17} = \{1,2,3\}\),
\(S_{18} = \{1,2,4\}\),
\(S_{19} = \{1,2,5\}\),
\(S_{20} = \{1,3,4\}\),
\(S_{21} = \{1,3,5\}\),
\(S_{22} = \{1,4,5\}\),
\(S_{23} = \{2,3,4\}\),
\(S_{24} = \{2,3,5\}\),
\(S_{25} = \{2,4,5\}\),
\(S_{26} = \{3,4,5\}\),
\(S_{27} = \{1,2,3,4\}\),
\(S_{28} = \{1,2,3,5\}\),
\(S_{29} = \{1,2,4,5\}\),
\(S_{30} = \{1,3,4,5\}\),
\(S_{31} = \{2,3,4,5\}\),
\(S_{32} = \{1,2,3,4,5\}\).
The half of 32 sets, 16 sets have an element 1, 2, 3, 4 and 5 respectively.
When we calculate \(A_1 + A_2 + \cdots + A_{32}\), 1 happens 16 times, 2 happens 16 times, ... and 5 happens 16 times.
Thay's why we have \(A_1 + A_2 + \cdots + A_{32} = 16*1 + 16*2 + ... + 16*5 = 16(1+2+3+4+5) = 16*15 = 240\).
Answer: D
General Discussion
GMAT 1: 760 Q51 V42
Posts: 10,057
=>
\(A\) has \(2^5 = 32\) subsets, so \(n = 32\). Each element of \(A\) is contained in \(2^{5-1} = 2^4 = 16\) subsets of \(A\) (We fix one element and find the number of subsets of the remaining elements). So, A1 + A2 + A3 + … + A32 = \(16*(1+2+3+4+5) = 240.\)
Therefore, the answer is D.
Answer: D
\(A\) has \(2^5 = 32\) subsets, so \(n = 32\). Each element of \(A\) is contained in \(2^{5-1} = 2^4 = 16\) subsets of \(A\) (We fix one element and find the number of subsets of the remaining elements). So, A1 + A2 + A3 + … + A32 = \(16*(1+2+3+4+5) = 240.\)
Therefore, the answer is D.
Answer: D
I did the other way round!
1) Calculated the sum of set A= 15.
2) tried dividing answers by 15.
3) integer answer was answer D
Posted from my mobile device
1) Calculated the sum of set A= 15.
2) tried dividing answers by 15.
3) integer answer was answer D
Posted from my mobile device
tgubbay1
Joined: 13 Nov 2014
Last visit: 04 Sep 2025
Posts: 28
Location: France
Concentration: Healthcare, Statistics
Schools: HBS '25 (D) Booth '25 (A) Wharton '25 (D) Sloan '25 (D) CBS '25 (WD) Haas '25 (WD) Stern '25 (WD) Kellogg '25 (WD) Stanford '25 (WD)
WE:Consulting (Consulting)
this question is terribly worded, didn't understand it at all. Can you explain why there are 2 elements in your subset?
Posts: 28
MathRevolution
Can you please explain how and why we need to get subsets? Is there a particular formula for solving this type of question?
warrior1991
Joined: 03 Mar 2017
Last visit: 03 Feb 2022
Posts: 537
Location: India
Concentration: Operations, Technology
Products:
Posts: 537
nsdl1985
210 also gets divided by 15. Hence B can also an answer in this case.
GMAT 1: 760 Q51 V42
Posts: 10,057
syedazeem3
\(A_i\)'s are the sums of elements of subsets. That's why we should consider subsets.
Please review the previous solution.
Posts: 175
MathRevolution
Is this really a GMAT type ques ? Seems to be really tough and have not seen this concept covered in OG
Posts: 175
nsdl1985
then by this standard, even B can be answer . Any reason to eliminate B ?
GMAT 1: 760 Q51 V42
Posts: 10,057
MathRevolution
It is a question related to counting.
It is a scope of GMAT exam.
Lord_Biplab
Joined: 27 May 2024
Last visit: 03 Mar 2026
Posts: 30
Location: India
Concentration: General Management, Operations
Schools: IIMA '26 (D) IIMB '26 (D) IIM (II)
GRE 1: Q166 V159
GPA: 3
WE:Operations (Energy)
Updated on: 27 Jul 2024, 07:25
Originally posted by Lord_Biplab on 19 Jul 2024, 07:41.
Last edited by Lord_Biplab on 27 Jul 2024, 07:25, edited 1 time in total.
Last edited by Lord_Biplab on 27 Jul 2024, 07:25, edited 1 time in total.
Total number of subsets possible for a set containing 5 elements = \(2^5\) = \(32\).
Probable sum of the elements = \(\frac{(1+2+3+4+5)}{2}\) = \(\frac{15}{2}\)
Probable sum has denominator 2 instead of 5 because the sum of number of subsets is a distribution that is symmetrical about the middle.
e.g.: sum of subsets {0} and {1,2,3,4,5} = 15.
sum of subsets {1} and {2,3,4,5} = 15.
sum of subsets {1,2,3} and {4,5} =15, and so on.
Thus, sum of the elements of subsets = 32 \(*\) 7.5 = 240.
Probable sum of the elements = \(\frac{(1+2+3+4+5)}{2}\) = \(\frac{15}{2}\)
Probable sum has denominator 2 instead of 5 because the sum of number of subsets is a distribution that is symmetrical about the middle.
e.g.: sum of subsets {0} and {1,2,3,4,5} = 15.
sum of subsets {1} and {2,3,4,5} = 15.
sum of subsets {1,2,3} and {4,5} =15, and so on.
Thus, sum of the elements of subsets = 32 \(*\) 7.5 = 240.
jack5397
Joined: 13 Sep 2020
Last visit: 01 Jun 2026
Posts: 112
Location: India
Concentration: General Management, Strategy
Schools: ISB '27 IIMA '26 INSEAD '26
GMAT Focus 1: 575 Q79 V79 DI77
GMAT Focus 2: 575 Q80 V81 DI75
GMAT Focus 3: 635 Q82 V83 DI79
GMAT 1: 460 Q36 V18 (Online)
GPA: 3.8
Products:
Schools: ISB '27 IIMA '26 INSEAD '26
GMAT Focus 3: 635 Q82 V83 DI79
GMAT 1: 460 Q36 V18 (Online)
Posts: 112
MathRevolution
Bunuel can you pls help on this question. I understand why he got 32 subsets but unable to understand why he divided by 2 to get 16 subsets. Also if you have any alternate method it would be really helpful.
Thank you
Automated notice from GMAT Club BumpBot:
A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.
This post was generated automatically.
_________________
A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.
This post was generated automatically.
_________________
Moderator:
Announcements
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.