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.
Apr 2610:00 AM EDT
-11:00 AM EDT
The Target Test Prep course represents a quantum leap forward in GMAT preparation, a radical reinterpretation of the way that students should study. Try before you buy with a 5-day, full-access trial of the course for FREE!
Apr 2711:00 AM EDT
-12:00 PM EDT
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors
Apr 2808:00 AM PDT
-11:00 AM PDT
Whether you are just beginning your MBA journey or fine-tuning your path to a 700+ score, GMAT Day is designed to give you a competitive edge.
Updated on: 19 Jul 2024, 08:42
Originally posted by MathRevolution on 01 Sep 2019, 22:59.
Last edited by Bunuel on 19 Jul 2024, 08:42, edited 2 times in total.
Last edited by Bunuel on 19 Jul 2024, 08:42, edited 2 times in total.
Kudos
Bookmarks
D
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%
(02:43)
wrong
based on 206
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?
\(A. 200\)
\(B. 210\)
\(C. 230\)
\(D. 240\)
\(E. 250\)
\(A. 200\)
\(B. 210\)
\(C. 230\)
\(D. 240\)
\(E. 250\)
08 Sep 2019, 16:16
Kudos
Bookmarks
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
01 Sep 2019, 23:00
Kudos
Bookmarks
=>
\(A\) 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
