GRE Prep 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.
Retired Moderator
Joined: 19 Nov 2020
Posts: 326
Given Kudos: 64
GRE 1: Q160 V152
What is the resultant interquartile range for a set of unique positive
[#permalink]
24 Sep 2021, 07:19
24 Sep 2021, 07:19
2
3
Bookmarks
00:00
Question Stats:
70% (01:35) correct
30% (02:45) wrong based on 10 sessions
Hide Show timer Statistics
What is the resultant Inter-Quartile range for a set of unique positive values, if the values in the top 50-percentile are decreased by 3 and then divided by 5, while the values in the bottom 50 percentile (median included) are divided by 5 and then reduced by 3, given the original Inter-Quartile range was 48?
(A) 8
(B) 10
(C) 12
(D) 14
(E) 16
Source: Scholarden
p.s. I have spent 4-5 minutes trying to figure out and solve this question. It's an awesome one
(A) 8
(B) 10
(C) 12
(D) 14
(E) 16
Source: Scholarden
p.s. I have spent 4-5 minutes trying to figure out and solve this question. It's an awesome one
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Given Kudos: 172
Location: India
WE:Education (Education)
What is the resultant interquartile range for a set of unique positive
[#permalink]
28 Sep 2021, 11:12
28 Sep 2021, 11:12
2
motion2020 wrote:
What is the resultant Inter-Quartile range for a set of unique positive values, if the values in the top 50-percentile are decreased by 3 and then divided by 5, while the values in the bottom 50 percentile (median included) are divided by 5 and then reduced by 3, given the original Inter-Quartile range was 48?
(A) 8
(B) 10
(C) 12
(D) 14
(E) 16
Source: Scholarden
p.s. I have spent 4-5 minutes trying to figure out and solve this question. It's an awesome one
(A) 8
(B) 10
(C) 12
(D) 14
(E) 16
Source: Scholarden
p.s. I have spent 4-5 minutes trying to figure out and solve this question. It's an awesome one
Refer to the figure below;
Old IQR = \((x - y) = 48\)
New IQR = \(\frac{(x - 3)}{5} - (\frac{y}{5} - 3)\)
= \(\frac{x}{5} - \frac{y}{5} + 3 - \frac{3}{5}\)
= \(\frac{{(x - y) + 12}}{5} = \frac{{48 + 12}}{5} = \frac{60}{5} = 12\)
Hence, option C
Attachments
What is the resultant Inter-Quartile range.png [ 4.08 KiB | Viewed 2633 times ]
General Discussion
Moderator
Joined: 02 Jan 2020
Status:GRE Quant Tutor
Posts: 1141
Given Kudos: 9
Location: India
Concentration: General Management
Schools: XLRI Jamshedpur, India - Class of 2014
GMAT 1: 700 Q51 V31
GPA: 2.8
WE:Engineering (Computer Software)
What is the resultant interquartile range for a set of unique positive
[#permalink]
19 Oct 2022, 09:04
19 Oct 2022, 09:04
Given that Original IQR (Inter-Quartile range) = 48
We know that IQR = \(Q_3\) - \(Q_1\) (Third Quartile - First Quartile) = 48
Now, all the values in the top 50% are decreased by 3 and then divided by 5
=> Value of \(Q_3\) which is also the middle value between \(Q_2\) and the highest value will also get decreased by 3 and then divided by 5
=> New \(Q_3\) = \(\frac{Q_3 - 3}{5}\) = \(\frac{Q_3}{5}\) - \(\frac{3}{5}\)
Now, all the values in the bottom 50% are divided by 5 and then reduced by 3
=> Value of \(Q_1\) which is also the middle value between Minimum value and \(Q_2\) will also get divided by 5 and then reduced by 3
=> New \(Q_1\) = \(\frac{Q_1}{5}\) - 3
=> New IQR = New \(Q_3\) - New \(Q_1\) = \(\frac{Q_3}{5}\) - \(\frac{3}{5}\) - (\(\frac{Q_1}{5}\) - 3)
= \(\frac{Q_3 - Q_1}{5}\) - \(\frac{3}{5}\) + 3
= \(\frac{48}{5}\) - \(\frac{3}{5}\) + 3
= \(\frac{48 - 3}{5}\) + 3
= 9 + 3 = 12
So, Answer will be C
Hope it helps!
Watch the following video to learn the Basics of Box and Whisker Plot
We know that IQR = \(Q_3\) - \(Q_1\) (Third Quartile - First Quartile) = 48
Now, all the values in the top 50% are decreased by 3 and then divided by 5
=> Value of \(Q_3\) which is also the middle value between \(Q_2\) and the highest value will also get decreased by 3 and then divided by 5
=> New \(Q_3\) = \(\frac{Q_3 - 3}{5}\) = \(\frac{Q_3}{5}\) - \(\frac{3}{5}\)
Now, all the values in the bottom 50% are divided by 5 and then reduced by 3
=> Value of \(Q_1\) which is also the middle value between Minimum value and \(Q_2\) will also get divided by 5 and then reduced by 3
=> New \(Q_1\) = \(\frac{Q_1}{5}\) - 3
=> New IQR = New \(Q_3\) - New \(Q_1\) = \(\frac{Q_3}{5}\) - \(\frac{3}{5}\) - (\(\frac{Q_1}{5}\) - 3)
= \(\frac{Q_3 - Q_1}{5}\) - \(\frac{3}{5}\) + 3
= \(\frac{48}{5}\) - \(\frac{3}{5}\) + 3
= \(\frac{48 - 3}{5}\) + 3
= 9 + 3 = 12
So, Answer will be C
Hope it helps!
Watch the following video to learn the Basics of Box and Whisker Plot
