During an experiment, some water was removed from each of : Data Sufficiency (DS)

cipher

Manager

Joined: 25 Jun 2009

Posts: 132

Own Kudos [?]: 333 [3]

Given Kudos: 6

Q49 V22 GMAT 2: 700 Q50 V35

Send PM

Re: GMAT Prep DS Q [#permalink]

13 May 2010, 05:04

3

Kudos

vaivish1723 wrote:

Hi,
I have attached few gmat prep DS Qs. Please respond with explanations. Apology if there is duplications.

Ans A

SD doesnt change when we add/subtract the same amount from all the values in the set.

Please see this link by Bunuel, it will help in understanding concepts regarding SD.

ps-questions-about-standard-deviation-85897.html

amannain1

Intern

Joined: 07 Sep 2010

Posts: 8

Own Kudos [?]: 6 [3]

Given Kudos: 8

Send PM

Re: GMAT Prep DS Q [#permalink]

03 Nov 2010, 00:17

3

Kudos

Hi Nitish,
Answer is indeed A but SD will change.
It should be now 30% less than before.

As bunuel has listed in point#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."

--
Aman

B

kraizada84

Manager

Joined: 13 Mar 2012

Posts: 155

Own Kudos [?]: 473 [3]

Given Kudos: 48

Concentration: Operations, Strategy

Send PM

Re: Standard Deviation [#permalink]

22 Mar 2012, 03:22

3

Kudos

imadkho wrote:

During an experiment, some water was removed from each of 6 water tanks. If the standard deviation of the volume of water in the tanks at the beginning of the experiment was 10 gallons, what was the standard deviation of the volumes of water in the tanks at the end of the experiment ?
1- For each tank, 30% of the volume of water that was in the tank at the beginning of the experiment was removed during the experiment.
2- The average (arithmetic mean) volume of water in the tanks at the end of the experiment was 63 gallons.

This question is similar to :

set X=(A,B,C,D,E,F)
SD= 10

Whats the SD when
set X=(A-a),(B-b),.....(F-f)

statement 1:
a=0.3A
SIMILARILY FOR OTHERS

hence we can find the value for this list.
SUFFICIENT

statement 2: INSUFFICIENT

as only knowing AM at the end of operation couldnot give any information for the reductions in the value of individual element

hence A

imadkho

Intern

Joined: 30 Nov 2011

Posts: 14

Own Kudos [?]: 231 [0]

Given Kudos: 23

Location: United States

GMAT 1: 700 Q47 V38

GPA: 3.54

Send PM

Re: During an experiment, some water was removed from each of [#permalink]

22 Mar 2012, 07:05

Dear Bunuel, your explanation is great, but if I got you right, then based on the first statement, the standard deviation of the volumes at the end of the experiment should be also 10 (and not 7), as it was at the beginning of the experiment.

L

Bunuel

Math Expert

Joined: 02 Sep 2009

Posts: 92915

Own Kudos [?]: 619011 [1]

Given Kudos: 81595

Send PM

Re: During an experiment, some water was removed from each of [#permalink]

22 Mar 2012, 08:05

1

Bookmarks

Expert Reply

imadkho wrote:

Dear Bunuel, your explanation is great, but if I got you right, then based on the first statement, the standard deviation of the volumes at the end of the experiment should be also 10 (and not 7), as it was at the beginning of the experiment.

If we add or subtract a constant to each term in a set:
SD will not change.

If we increase or decrease each term in a set by the same percent (multiply all terms by the constant):
SD will increase or decrease by the same percent.

Since (1) says that for each tank 30% of the water was removed then the SD will decrease by the same 30%.

imadkho

Intern

Joined: 30 Nov 2011

Posts: 14

Own Kudos [?]: 231 [0]

Given Kudos: 23

Location: United States

GMAT 1: 700 Q47 V38

GPA: 3.54

Send PM

Re: During an experiment, some water was removed from each of [#permalink]

22 Mar 2012, 10:51

Bunuel, it seems I am not getting you correctly. You are saying that SD will not change if a constant is added to/subtrated from the members of any list (I agree), so how come you are also telling me that SD will go down by 30% by the end of the experiment. I think it should also stay the same.
thanks

L

Bunuel

Math Expert

Joined: 02 Sep 2009

Posts: 92915

Own Kudos [?]: 619011 [0]

Given Kudos: 81595

Send PM

Re: During an experiment, some water was removed from each of [#permalink]

22 Mar 2012, 11:01

Expert Reply

imadkho wrote:

Bunuel, it seems I am not getting you correctly. You are saying that SD will not change if a constant is added to/subtrated from the members of any list (I agree), so how come you are also telling me that SD will go down by 30% by the end of the experiment. I think it should also stay the same.
thanks

In this case we are not subtracting a constant from each term, we are decreasing each term by some percent (multiplying by 0.7) and if we increase or decrease each term in a set by the same percent (multiply all terms by the constant): SD will increase or decrease by the same percent.

Edvento

Manager

Joined: 08 Apr 2012

Posts: 95

Own Kudos [?]: 227 [4]

Given Kudos: 14

Send PM

Re: Standard Deviation question [#permalink]

16 Jun 2012, 01:46

3

Kudos

1

Bookmarks

riteshgupta wrote:

Can any one answer the below with a bit of detail, so that S.D concept is cleared????

During an experiment, some water was removed from each of 6 water tanks. If the standard deviation of the volumes of water in the tanks at the beginning of the experiment was 10 gallons, what was the standard deviation of the volumes of water in the tanks at the end of the experiment?

(1) For each tank, 30 percent of the volume of water that was in the tank at the beginning of the experiment was removed during the experiment.

(2) The average (arithmetic mean) volume of water in the tanks at the end of the experiment was 63 gallons.

We have

Standard Deviation = \(\sigma =\sqrt{{\frac{1}{6}}*[(x_1 - M)^2 + (x_2 - M)^2 + ... + (x_6 - M)^2} = 10\)

Here \(M\) is the mean.

The subscript 6 is for the 6 water tanks

Now,

Evaluating statement 1 only

For each tank 30% of the water was removed.

The mean becomes \((1- \frac{30}{100})M = 0.7M\)

Also each of \(x_1, x_2, ..., x_6\) becomes \(0.7x_1, 0.7x_2, ..., 0.7x_6\) respectively.

Hence,

Standard Deviation = \(\sigma =0.7* \sqrt{{\frac{1}{6}}*[(x_1 - M)^2 + (x_2 - M)^2 + ... + (x_6 - M)^2} = 0.7*10 = 7\)

Hence this statement alone is sufficient.

Choices B, C, E are eliminated.

Evaluating statement 2 only

The mean after the reduction, \(M = 63\) gallons.

We have no idea of the initial value of \(M\) or \(x_1, x_2, ..., x_6\) or how these values have changed.

Hence, this statement alone is insufficient.

Choice D is ruled out.

Answer is A.

Regards,

Shouvik.

B

NoHalfMeasures

Retired Moderator

Joined: 29 Oct 2013

Posts: 220

Own Kudos [?]: 2006 [2]

Given Kudos: 204

Concentration: Finance

GPA: 3.7

WE:Corporate Finance (Retail Banking)

Send PM

Re: During an experiment, some water was removed from each of [#permalink]

19 Nov 2013, 07:47

2

Bookmarks

Here is a neat rule I keep handy when dealing with statistics problems on the GMAT:
” If X is added/subtracted to/from every element of a set, all 3 measures of Central Tendency- mean, median, mode- will be added/subtracted by X, whereas measures of Dispersion- range, interquartile range and standard deviation, variance will be unaffected. On the other hand, if every element is multiplied by X, both measures of central tendency and dispersion will be multiplied by X” -

Hope it helps others.

B

nidhiprasad

Intern

Joined: 03 Apr 2018

Posts: 9

Own Kudos [?]: 3 [0]

Given Kudos: 98

Send PM

Re: During an experiment, some water was removed from each of [#permalink]

22 May 2018, 06:44

Question : If the mean is 10 and number of numbers is n . Now the new mean is 15 and number of numbers remain same . How does this information affect the SD. is this information sufficient to comment on SD?

L

KarishmaB

Tutor

Joined: 16 Oct 2010

Posts: 14823

Own Kudos [?]: 64922 [1]

Given Kudos: 426

Location: Pune, India

Send PM

Re: During an experiment, some water was removed from each of [#permalink]

22 May 2018, 07:14

1

Kudos

Expert Reply

nidhiprasad wrote:

Question : If the mean is 10 and number of numbers is n . Now the new mean is 15 and number of numbers remain same . How does this information affect the SD. is this information sufficient to comment on SD?

No. SD does not depend on the actual mean. It depends on the distance of the numbers from mean and the number of numbers.
Check this post:
https://gmatclub.com/forum/during-an-ex ... ml#p831904

B

Gijmaja

Intern

Joined: 24 Sep 2022

Posts: 30

Own Kudos [?]: 3 [0]

Given Kudos: 9

Location: Georgia

Schools: Booth '25 Anderson '25 (WL) Darden '25

GMAT 1: 720 Q50 V38

GPA: 3.71

Send PM

Re: During an experiment, some water was removed from each of [#permalink]

09 Dec 2022, 00:26

Bunuel wrote:

During an experiment, some water was removed from each of the 6 water tanks. If the standard deviation of the volumes of water in the tanks at the beginning of the experiment was 10 gallons, what was the standard deviation of the volumes of water in the tanks at the end of the experiment?

(1) For each tank, 30% of the volume of water that was in the tank at the beginning of the experiment was removed during the experiment.
(2) The average (arithmetic mean) volume of water in the tanks at the end of the experiment was 63 gallons.

You should know that:
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.

If we increase or decrease each term in a set by the same percent (multiply all terms by the constant):
Mean will increase or decrease by the same percent.
SD will increase or decrease by the same percent.

You can check it yourself:
SD of a set: {1,1,4} will be the same as that of {5,5,8} as second set is obtained by adding 4 to each term of the first set.

That's because Standard Deviation shows how much variation there is from the mean. And when adding or subtracting a constant to each term we are shifting the mean of the set by this constant (mean will increase or decrease by the same constant) but the variation from the mean remains the same as all terms are also shifted by the same constant.

So according to this rules statement (1) is sufficient to get new SD, it'll be 30% less than the old SD so 7. As for statement (2) it's clearly insufficient as knowing mean gives us no help in getting new SD.

Answer: A.

For more on this check Standard Deviation chapter of Math Book: https://gmatclub.com/forum/math-standar ... 87905.html

Collection of PS questions on SD: https://gmatclub.com/forum/ps-questions ... 85897.html
Collection of PS questions on SD: https://gmatclub.com/forum/ds-questions ... 85896.html

Hope it's clear.

I seem to misunderstand an important information. Did you assume that the water tanks were of the same size? Nowhere does the problem state that.

Now imagine if tanks were of the following volumes: 4, 6, 8, 10. St. dev is 2.58.
reduce the water in the tank by 30%: 2.8, 4.2, 5.6, 7. St. dev is 1.81.

Can you expand on this matter?

L

KarishmaB

Tutor

Joined: 16 Oct 2010

Posts: 14823

Own Kudos [?]: 64922 [2]

Given Kudos: 426

Location: Pune, India

Send PM

Re: During an experiment, some water was removed from each of [#permalink]

09 Dec 2022, 01:21

2

Kudos

Expert Reply

Gijmaja wrote:

Bunuel wrote:

During an experiment, some water was removed from each of the 6 water tanks. If the standard deviation of the volumes of water in the tanks at the beginning of the experiment was 10 gallons, what was the standard deviation of the volumes of water in the tanks at the end of the experiment?

(1) For each tank, 30% of the volume of water that was in the tank at the beginning of the experiment was removed during the experiment.
(2) The average (arithmetic mean) volume of water in the tanks at the end of the experiment was 63 gallons.

You should know that:
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.

If we increase or decrease each term in a set by the same percent (multiply all terms by the constant):
Mean will increase or decrease by the same percent.
SD will increase or decrease by the same percent.

You can check it yourself:
SD of a set: {1,1,4} will be the same as that of {5,5,8} as second set is obtained by adding 4 to each term of the first set.

That's because Standard Deviation shows how much variation there is from the mean. And when adding or subtracting a constant to each term we are shifting the mean of the set by this constant (mean will increase or decrease by the same constant) but the variation from the mean remains the same as all terms are also shifted by the same constant.

So according to this rules statement (1) is sufficient to get new SD, it'll be 30% less than the old SD so 7. As for statement (2) it's clearly insufficient as knowing mean gives us no help in getting new SD.

Answer: A.

For more on this check Standard Deviation chapter of Math Book: https://gmatclub.com/forum/math-standar ... 87905.html

Collection of PS questions on SD: https://gmatclub.com/forum/ps-questions ... 85897.html
Collection of PS questions on SD: https://gmatclub.com/forum/ds-questions ... 85896.html

Hope it's clear.

I seem to misunderstand an important information. Did you assume that the water tanks were of the same size? Nowhere does the problem state that.

Now imagine if tanks were of the following volumes: 4, 6, 8, 10. St. dev is 2.58.
reduce the water in the tank by 30%: 2.8, 4.2, 5.6, 7. St. dev is 1.81.

Can you expand on this matter?

There was no assumption made about the size of the tank nor about the amount of the water in each tank.

The volume of water in each tank could have been any random number. What we do know is that their SD is 10.

What happens when each value in the list is reduced by 30% i.e. it becomes 70% of its initial value? Each value will be multiplied by 0.7. Then the mean will be multiplied by 0.7 too and the SD will get multiplied by 0.7 too.
The same is illustrated by your example too since 1.81 is 70% of 2.58.

So when we multiply each value of a list by the same positive number, the SD gets multiplied by the same number too.
So if the old SD of a set is 10 and if each value is reduced by 30% i.e. multiplied by 0.7, the new Sd will also get multiplied by 0.7 i.e. it will become 7.

B

nikitathegreat

Manager

Joined: 16 Dec 2021

Posts: 108

Own Kudos [?]: 15 [0]

Given Kudos: 43

Location: India

Schools: ISB '23 LBS '24 NTU NUS Said '23

GMAT 1: 630 Q45 V31

Send PM

Re: During an experiment, some water was removed from each of [#permalink]

14 Jun 2023, 12:28

Bunuel wrote:

During an experiment, some water was removed from each of the 6 water tanks. If the standard deviation of the volumes of water in the tanks at the beginning of the experiment was 10 gallons, what was the standard deviation of the volumes of water in the tanks at the end of the experiment?

(1) For each tank, 30% of the volume of water that was in the tank at the beginning of the experiment was removed during the experiment.
(2) The average (arithmetic mean) volume of water in the tanks at the end of the experiment was 63 gallons.

You should know that:
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.

If we increase or decrease each term in a set by the same percent (multiply all terms by the constant):
Mean will increase or decrease by the same percent.
SD will increase or decrease by the same percent.

You can check it yourself:
SD of a set: {1,1,4} will be the same as that of {5,5,8} as second set is obtained by adding 4 to each term of the first set.

That's because Standard Deviation shows how much variation there is from the mean. And when adding or subtracting a constant to each term we are shifting the mean of the set by this constant (mean will increase or decrease by the same constant) but the variation from the mean remains the same as all terms are also shifted by the same constant.

So according to this rules statement (1) is sufficient to get new SD, it'll be 30% less than the old SD so 7. As for statement (2) it's clearly insufficient as knowing mean gives us no help in getting new SD.

Answer: A.

For more on this check Standard Deviation chapter of Math Book: https://gmatclub.com/forum/math-standar ... 87905.html

Collection of PS questions on SD: https://gmatclub.com/forum/ps-questions ... 85897.html
Collection of PS questions on SD: https://gmatclub.com/forum/ds-questions ... 85896.html

Hope it's clear.

In the first statement, do we mean 30% water of all the six tanks were removed from each of the tank or 30% water from each tank. If we mean latter, then in that scenario, each tank can have different volume of water and 30% of each volume of water would mean different. Please help me explain the language

B

Mrinal98

Intern

Joined: 20 Sep 2022

Posts: 1

Own Kudos [?]: 0 [0]

Given Kudos: 15

Send PM

Re: During an experiment, some water was removed from each of [#permalink]

17 Aug 2023, 04:43

Bunuel statement 1 says "30% of the volume of water that was in the tank at the beginning of the experiment was removed". Are we to assume that each of the 6 tankers had equal gallons of water as it is nowhere mentioned in the question.
if we take a different value for each of the 6 tankers then the "30%" value will not be a constant and hence statement 1 would not be sufficient.

Please correct me where I'm thinking wrong..

L

Bunuel

Math Expert

Joined: 02 Sep 2009

Posts: 92915

Own Kudos [?]: 619011 [1]

Given Kudos: 81595

Send PM

Re: During an experiment, some water was removed from each of [#permalink]

17 Aug 2023, 04:59

1

Kudos

Expert Reply

Mrinal98 wrote:

Bunuel statement 1 says "30% of the volume of water that was in the tank at the beginning of the experiment was removed". Are we to assume that each of the 6 tankers had equal gallons of water as it is nowhere mentioned in the question.
if we take a different value for each of the 6 tankers then the "30%" value will not be a constant and hence statement 1 would not be sufficient.

Please correct me where I'm thinking wrong..

Yes, we are not told that each tank contained an equal amount of water, but it does not matter. Regardless of the initial amounts in the tanks, after the removal, they would contain 0.7 times their original volume. This means that the standard deviation would become 0.7 times its original value. When each term in a set is multiplied by a constant, like 0.7 in this case, the standard deviation also gets multiplied by the same constant.

gmatclubot

Re: During an experiment, some water was removed from each of [#permalink]

17 Aug 2023, 04:59

GMAT Data Sufficiency (DS) Questions

During an experiment, some water was removed from each of