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.
Nov 2211:00 AM IST
-01:00 PM IST
Do RC/MSR passages scare you? e-GMAT is conducting a masterclass to help you learn – Learn effective reading strategies Tackle difficult RC & MSR with confidence Excel in timed test environment- Nov 23
11:00 AM IST
-01:00 PM IST
Attend this free GMAT Algebra Webinar and learn how to master the most challenging Inequalities and Absolute Value problems with ease. 
Nov 2510:00 AM EST
-11:00 AM EST
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.
kiran120680
Moderator - Masters Forum
Joined: 18 Feb 2019
Last visit: 27 Jul 2022
Posts: 706
Given Kudos: 276
Location: India
Schools: AGSM '20 EDHEC Sept 2019 Intake Great Lakes '21 IE
GMAT 1: 460 Q42 V13
GPA: 3.6
13 Jun 2019, 09:13
Kudos
Bookmarks
A
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:
45% (02:39) correct
55%
(02:54)
wrong
based on 297
sessions
History
Date
Time
Result
Not Attempted Yet
List A ={1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
The integers from list A are used to form two distinct sets P and Q each consisting of distinct integers only. If all the integers from list A are used at least once and none of the integers are used more than twice, how many integers from list A are used more than once?
1) The numbers of integers in sets P and Q are, respectively, 2 and 3 less than the number of integers in list A.
2) The difference between the sum of the integers in sets P and Q and the sum of the integers in list A is 15.
The integers from list A are used to form two distinct sets P and Q each consisting of distinct integers only. If all the integers from list A are used at least once and none of the integers are used more than twice, how many integers from list A are used more than once?
1) The numbers of integers in sets P and Q are, respectively, 2 and 3 less than the number of integers in list A.
2) The difference between the sum of the integers in sets P and Q and the sum of the integers in list A is 15.
13 Jun 2019, 10:31
Kudos
Bookmarks
Statement 1- Elements in set P= 10-2=8, Elements in set Q=10-3=7
Number of integers from list A are used more than once= 8+7-10=5 (sufficient)
Statement 2- The difference between the sum of the integers in sets P and Q and the sum of the integers in list A is 15.
Or sum of the integers of set A that are used more than once is 15
1. 15= 1+2+3+4+5
In this case, integers from list A are used more than once are 5
2. 15= 2+3+4+6
In this case, integers from list A are used more than once are 4
Statement 2 - Insufficient
Number of integers from list A are used more than once= 8+7-10=5 (sufficient)
Statement 2- The difference between the sum of the integers in sets P and Q and the sum of the integers in list A is 15.
Or sum of the integers of set A that are used more than once is 15
1. 15= 1+2+3+4+5
In this case, integers from list A are used more than once are 5
2. 15= 2+3+4+6
In this case, integers from list A are used more than once are 4
Statement 2 - Insufficient
kiran120680
vinayakvaish
Joined: 29 May 2018
Last visit: 19 Oct 2020
Posts: 91
Given Kudos: 52
Location: India
Schools: Marshall '22 (A$) IIMA PGPX "21 (D) Duke '22 (D) IIMB EPGP "21 (A) McCombs '22 (A) IIMC MBAEx "21 (WD) Georgia Tech '22 (A$) Johnson '22 (WD)
GMAT 1: 700 Q48 V38
GMAT 2: 720 Q49 V39
GPA: 4
Schools: Marshall '22 (A$) IIMA PGPX "21 (D) Duke '22 (D) IIMB EPGP "21 (A) McCombs '22 (A) IIMC MBAEx "21 (WD) Georgia Tech '22 (A$) Johnson '22 (WD)
GMAT 2: 720 Q49 V39
Posts: 91
14 Jun 2019, 05:01
Kudos
Bookmarks
Hi please consider this:
Set A {1,2,3,4,5,6,7,8,9,10} from which two sets have to be created which contain distinct integers only. To find integers used twice, we have to look for overlaps in set p and set q
Statement 1: Set P has 8 elements whereas Set Q has 7
Set P can be {1,2,3,4,5,6,7,8} and Set Q can be {1,2,3,4,5,6,7}- overlap of 7 integers
Set P can also be {1,2,3,4,5,6,7,8} and Set Q {10,9,8,7,6,5,4} - overlap of 5 integers
Since it is given that each integer from Set A has to be used at least once hence we take the second case
Statement 1 is sufficient
Statement 2:
Sum of P+Q - Sum of A=15
15 can be the sum of 5 distinct integers at max ie. 1,2,3,4,5 but since we are not given how many elements to choose the elements may well be 4,5,6
Statement 2 is not Sufficient
In case the "must be used once" condition was absent in Set A, then Statement 1 would have gotten interesting.
Max overlap is 7 and Minimum overlap is 5 between two 7 and 8 element sets. Then Statement 1 would be insufficient and you would have to use the fact that sum of 15 can be achieved by a maximum of 5 distinct positive integers {1,2,3,4,5,}
Hence then the Answer would have been C
Here of course the Answer is A
Set A {1,2,3,4,5,6,7,8,9,10} from which two sets have to be created which contain distinct integers only. To find integers used twice, we have to look for overlaps in set p and set q
Statement 1: Set P has 8 elements whereas Set Q has 7
Set P can be {1,2,3,4,5,6,7,8} and Set Q can be {1,2,3,4,5,6,7}- overlap of 7 integers
Set P can also be {1,2,3,4,5,6,7,8} and Set Q {10,9,8,7,6,5,4} - overlap of 5 integers
Since it is given that each integer from Set A has to be used at least once hence we take the second case
Statement 1 is sufficient
Statement 2:
Sum of P+Q - Sum of A=15
15 can be the sum of 5 distinct integers at max ie. 1,2,3,4,5 but since we are not given how many elements to choose the elements may well be 4,5,6
Statement 2 is not Sufficient
In case the "must be used once" condition was absent in Set A, then Statement 1 would have gotten interesting.
Max overlap is 7 and Minimum overlap is 5 between two 7 and 8 element sets. Then Statement 1 would be insufficient and you would have to use the fact that sum of 15 can be achieved by a maximum of 5 distinct positive integers {1,2,3,4,5,}
Hence then the Answer would have been C
Here of course the Answer is A
