GMAT Changed on April 16th - Read about the latest changes here

It is currently 26 May 2018, 12:54

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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

The Department of Environmental Protection measured the volu

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Manager
Manager
avatar
Joined: 11 Aug 2011
Posts: 184
Location: United States
Concentration: Economics, Finance
GMAT Date: 10-16-2013
GPA: 3
WE: Analyst (Computer Software)
Reviews Badge
The Department of Environmental Protection measured the volu [#permalink]

Show Tags

New post Updated on: 18 May 2014, 05:11
11
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

58% (01:02) correct 42% (01:10) wrong based on 249 sessions

HideShow timer Statistics

The Department of Environmental Protection measured the volume of water in 10 similarly sized reservoirs in State X and found that the standard deviation of their volumes at the start of the year was 4 million cubic gallons. Was the standard deviation of those 10 volume measurements lower at the end of the year?

(1) At the end of the year, the average volume of the water in the 10 reservoirs had decreased by 20%.

(2) The percent decrease in the volume of the water in each reservoir during the year was the same.

I have issues solving such problems.
Can someone please let me know how do we solve such problems.

_________________

Kudos me if you like my post !!!!


Originally posted by akhil911 on 18 May 2014, 05:09.
Last edited by akhil911 on 18 May 2014, 05:11, edited 1 time in total.
1 KUDOS received
Manager
Manager
avatar
Joined: 11 Aug 2011
Posts: 184
Location: United States
Concentration: Economics, Finance
GMAT Date: 10-16-2013
GPA: 3
WE: Analyst (Computer Software)
Reviews Badge
Re: The Department of Environmental Protection measured the volu [#permalink]

Show Tags

New post 18 May 2014, 05:10
1
This post received
KUDOS
1
This post was
BOOKMARKED
Official solution provided by Veritas prep

This difficult data sufficiency question tests an important number property relating to standard deviation: if the terms in a set are each decreased by a fixed percentage, then the standard deviation decreases by that same percentage (unless the terms are all the same to begin with – then the standard deviation would be zero before the change and zero after). In the question stem you learn that the standard deviation of 10 measurements is 4 million at the beginning of the year (note – this guarantees that they are not all the same), and you must decide if that standard deviation had decreased at the end of the year. In statement (1) you learn that the average volume of the 10 reservoirs decreased by 20% over the year. Importantly this does NOT mean that each term decreased by 20%. A decrease in the average of all 10 volumes might yield a smaller standard deviation, but it could easily result in a larger standard deviation. Consider a sample set of 5, 10, and 15, which has an approximate standard deviation of 4. If the average of those 3 numbers is decreased by 20%, then the new set could be 5, 4, and 15 (average went from 10 to 8) and this set clearly has a higher standard deviation just by inspection (approximately 5 if you do the calculation). Remember that you do not need to calculate the standard deviation – just realize that you do not know how the set was changed to decrease the average, so you do not know the effect on the standard deviation. Statement (1) is not sufficient. With statement (2) you must be very careful as it appears to give you the information that was lacking in statement (1): it proves that each one had the same percentage decrease. At this point, many students will pick (C) as they fit together so nicely. However statement (2) is actually sufficient by itself: if the volume of each reservoir decreased by the same percentage (and the volume for each was not the same to begin with – something you know from the question stem) then the standard deviation MUST be lower after that change. It guarantees that the set “shrunk” during the year, reducing the dispersion and thus the standard deviation. Answer is B – statement 2 alone is sufficient.
_________________

Kudos me if you like my post !!!!

2 KUDOS received
Director
Director
User avatar
Joined: 25 Apr 2012
Posts: 702
Location: India
GPA: 3.21
WE: Business Development (Other)
Premium Member Reviews Badge
Re: The Department of Environmental Protection measured the volu [#permalink]

Show Tags

New post 18 May 2014, 07:39
2
This post received
KUDOS
1
This post was
BOOKMARKED
akhil911 wrote:
The Department of Environmental Protection measured the volume of water in 10 similarly sized reservoirs in State X and found that the standard deviation of their volumes at the start of the year was 4 million cubic gallons. Was the standard deviation of those 10 volume measurements lower at the end of the year?

(1) At the end of the year, the average volume of the water in the 10 reservoirs had decreased by 20%.

(2) The percent decrease in the volume of the water in each reservoir during the year was the same.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked
Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient
EACH statement ALONE is sufficient to answer the question asked
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed

I have issues solving such problems.
Can someone please let me know how do we solve such problems.



Here is quick summary for SD:

TIPS:
1. |Median-Mean| <= SD.

2. Variance is the square of the standard deviation.

3. If Range or SD of a list is 0, then the list will contain all identical elements. And vise versa: if a list contains all identical elements then the range and SD of a list is 0. If the list contains 1 element: Range is zero and SD is zero.

4. SD is always >=0. SD is 0 only when the list contains all identical elements (or which is same only 1 element).

5. Symmetric about the mean means that the shape of the distribution on the right and left side of the curve are mirror-images of each other.

6. If we add or subtract a constant to each term in a set:
Mean will increase or decrease by the same constant.
SD will not change.

7. If we increase or decrease each term in a set by the same percent:
Mean will increase or decrease by the same percent.
SD will increase or decrease by the same percent.


8. Changing the signs of the element of a set (multiplying by -1) has no effect on SD.

9. The SD of any list is not dependent on the average, but on the deviation of the numbers from the average. So just by knowing that two lists having different averages doesn't say anything about their standard deviation - different averages can have the same SD.

The above is from Math Expert Bunuel. It's very handy.
For more on this topic refer to

math-standard-deviation-87905.html
and
ps-questions-about-standard-deviation-85897.html

Coming back to the question

We need to find whether SD lower than what it was in the beginning of the year

St 1 says average vol of water had decreased by 20%. So if Total volume of water for 10 resevoirs was 100lts then at the end of the year Volume of 10 resevoirs was 80 lts.

Case 1 :Now Imagine if 9 resevoirs see an increase of 2 lts each and 1 resevoirs sees a decrease of 38 Lts then volume of water is still 80 lts (Average vol of water is 8 lts) but SD will be different (lower or more is not important)
Case 2:Also another case where each resevoir has volume of 10 lts each and each sees uniform decrease of 20% ie. at the end of the year each resevoir has 8 lts and Total volume is 80 lts and average volume is 8 ltr--------> In this case we can safely say SD is lower but not in Case 1

So ST 1 is not sufficient

Consider St 2 points out that each resevoir saw percent decrease and is pointing to Case 2 of St 1 and hence it is sufficient. It is in line with Pt 7
_________________


“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 45455
The Department of Environmental Protection measured the volu [#permalink]

Show Tags

New post 19 May 2014, 02:39
akhil911 wrote:
The Department of Environmental Protection measured the volume of water in 10 similarly sized reservoirs in State X and found that the standard deviation of their volumes at the start of the year was 4 million cubic gallons. Was the standard deviation of those 10 volume measurements lower at the end of the year?

(1) At the end of the year, the average volume of the water in the 10 reservoirs had decreased by 20%.

(2) The percent decrease in the volume of the water in each reservoir during the year was the same.

I have issues solving such problems.
Can someone please let me know how do we solve such problems.


Almost similar question to practice: during-an-experiment-some-water-was-removed-from-each-of-94166.html (GMAT Prep)

For more on that topic check Standard Deviation chapter of Math Book: math-standard-deviation-87905.html

Collection of PS questions on SD: ps-questions-about-standard-deviation-85897.html
Collection of DS questions on SD: ds-questions-about-standard-deviation-85896.html

Hope this helps.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
avatar
Joined: 21 Oct 2013
Posts: 189
Location: Germany
GMAT 1: 660 Q45 V36
GPA: 3.51
Re: The Department of Environmental Protection measured the volu [#permalink]

Show Tags

New post 08 Jul 2014, 03:55
I think on the GMAT it's not necessary to calculate the SD, just to basically know what it is. The SD gives us somehow the "distance" (deviation) between the mean of some data and each data point. Thus, if you only know something about the overall change and nothing about each data point, you can't tell whats happening with the SD. But if you know about each data point, you can answer if increase, decrease or stays same.

To the question:

(1) Here you only get to know the overall change of all data points. Wont help you to determine the SD. IS.
(2) Here they tell you that each reservoir as decreased in the same amount. This is enough to tell you that the SD will have decreased too.

Answer is B.
Intern
Intern
avatar
Joined: 26 Jul 2015
Posts: 2
GMAT ToolKit User Premium Member
Re: The Department of Environmental Protection measured the volu [#permalink]

Show Tags

New post 09 Aug 2015, 08:52
What if the decrease is 0%? Then the standard deviation does not change.
Retired Moderator
User avatar
Joined: 06 Jul 2014
Posts: 1262
Location: Ukraine
Concentration: Entrepreneurship, Technology
GMAT 1: 660 Q48 V33
GMAT 2: 740 Q50 V40
GMAT ToolKit User Premium Member
Re: The Department of Environmental Protection measured the volu [#permalink]

Show Tags

New post 09 Aug 2015, 09:09
steamtrain wrote:
What if the decrease is 0%? Then the standard deviation does not change.


Hello steamtrain
In this case they can not call it "decrease" and statement should be "The volume of the water in each reservoir during the year does not change"
_________________

Simple way to always control time during the quant part.
How to solve main idea questions without full understanding of RC.
660 (Q48, V33) - unpleasant surprise
740 (Q50, V40, IR3) - anti-debrief ;)

Current Student
avatar
S
Joined: 20 Mar 2014
Posts: 2644
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Premium Member Reviews Badge
The Department of Environmental Protection measured the volu [#permalink]

Show Tags

New post 09 Aug 2015, 13:04
Harley1980 wrote:
steamtrain wrote:
What if the decrease is 0%? Then the standard deviation does not change.


Hello steamtrain
In this case they can not call it "decrease" and statement should be "The volume of the water in each reservoir during the year does not change"


Calling it a decrease of 0% is not wrong. A 'decrease' can be of a 0 value of of 100 units. Calling a decrease =0 means that the net effect of the decrease was 0 or the quantity is question did not undergo any change.
Retired Moderator
User avatar
Joined: 06 Jul 2014
Posts: 1262
Location: Ukraine
Concentration: Entrepreneurship, Technology
GMAT 1: 660 Q48 V33
GMAT 2: 740 Q50 V40
GMAT ToolKit User Premium Member
Re: The Department of Environmental Protection measured the volu [#permalink]

Show Tags

New post 09 Aug 2015, 13:28
Engr2012 wrote:
Harley1980 wrote:
steamtrain wrote:
What if the decrease is 0%? Then the standard deviation does not change.


Hello steamtrain
In this case they can not call it "decrease" and statement should be "The volume of the water in each reservoir during the year does not change"


Calling it a decrease of 0% is not wrong. A 'decrease' can be of a 0 value of of 100 units. Calling a decrease =0 means that the net effect of the decrease was 0 or the quantity is question did not undergo any change.


Hello Engr2012
I will not argue that this is correct in real life (actually I hear about this first time, but I believe you because my learning of math begins from GMAT)

But as I know in GMAT each word of quantitative task should has some sense and in good task you will never meet information that has a purpose to throw you off.
So I think if we meet word decrease we shouldn't take into account possibility of 0.

Maybe you have some example of task in which decrease means 0?
_________________

Simple way to always control time during the quant part.
How to solve main idea questions without full understanding of RC.
660 (Q48, V33) - unpleasant surprise
740 (Q50, V40, IR3) - anti-debrief ;)

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 6858
Premium Member
Re: The Department of Environmental Protection measured the volu [#permalink]

Show Tags

New post 08 Apr 2018, 00:18
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: The Department of Environmental Protection measured the volu   [#permalink] 08 Apr 2018, 00:18
Display posts from previous: Sort by

The Department of Environmental Protection measured the volu

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.