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# During an experiment, some water was removed from each of

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Senior Manager
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During an experiment, some water was removed from each of [#permalink]

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13 May 2010, 04:07
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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.
Senior Manager
Joined: 25 Jun 2009
Posts: 287
Re: GMAT Prep DS Q [#permalink]

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13 May 2010, 05:04
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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.

Intern
Joined: 07 Sep 2010
Posts: 16
Re: GMAT Prep DS Q [#permalink]

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03 Nov 2010, 00:17
2
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
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8102
Location: Pune, India
Re: GMAT Prep DS Q [#permalink]

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12 Dec 2010, 04:36
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vaivish1723 wrote:
Hi,
I have attached few gmat prep DS Qs. Please respond with explanations. Apology if there is duplications.

Standard deviation measures dispersion around the mean i.e. how far apart the values are from mean. The actual calculation of the Standard Deviation is not asked in GMAT but you need to theoretically understand the concept.
e.g. If we are interested in SD of the following values:
2, 4, 5, 6, 8
Here, mean is 5.
At Veritas, we encourage you to visualize the numbers on a number line. The diagram below shows the 5 numbers with their mean 5. SD measures how far the numbers are from their mean.

Attachment:

Ques1.jpg [ 6.42 KiB | Viewed 38635 times ]

If we add 10 to each of the numbers, the numbers become:
12, 14, 15, 16, 18
New mean is 15 but relative to the new mean, the numbers are still dispersed in the say way around 15. So SD for these numbers is the same as SD above.

If we multiply/divide each number by some number, the SD changes. Look at the diagram below to understand why. If each number is multiplied by 3, the numbers are:
6, 12, 15, 18, 24

Attachment:

Ques2.jpg [ 6.51 KiB | Viewed 38637 times ]

On the number line, now they are much farther from their mean 15. Hence their SD is greater than before. It is actually 3 times the initial SD. (Check out the formula of SD to see why.)

In this question, initial SD was 10. When 30% of the water is removed from each tank, the leftover water is 70% i.e. 0.7*original volume of water. Since we are multiplying the original volume by 0.7, the SD will change. It will become 0.7*previous SD i.e. 0.7*10 = 7.

mehdiov: As we see from above, if we remove the same quantity, the SD will not change. Here we removed a fraction of the original quantity of each. e.g. if one tank had 50 gallons, we removed 30% i.e. 15 gallons. If another had 100 gallons, we removed 30 gallons.
_________________

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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Math Expert Joined: 02 Sep 2009 Posts: 46207 Re: GMAT Prep DS Q [#permalink] ### Show Tags 12 Dec 2010, 05:46 27 27 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: math-standard-deviation-87905.html Collection of PS questions on SD: ps-questions-about-standard-deviation-85897.html Collection of PS questions on SD: ds-questions-about-standard-deviation-85896.html Hope it's clear. _________________ Senior Manager Joined: 13 Mar 2012 Posts: 298 Concentration: Operations, Strategy Re: Standard Deviation [#permalink] ### Show Tags 22 Mar 2012, 03:22 3 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 _________________ Practice Practice and practice...!! If my reply /analysis is helpful-->please press KUDOS If there's a loophole in my analysis--> suggest measures to make it airtight. Intern Joined: 30 Nov 2011 Posts: 29 Location: United States GMAT 1: 700 Q47 V38 GPA: 3.54 Re: During an experiment, some water was removed from each of [#permalink] ### Show Tags 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. Math Expert Joined: 02 Sep 2009 Posts: 46207 Re: During an experiment, some water was removed from each of [#permalink] ### Show Tags 22 Mar 2012, 08:05 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%. _________________ Intern Joined: 30 Nov 2011 Posts: 29 Location: United States GMAT 1: 700 Q47 V38 GPA: 3.54 Re: During an experiment, some water was removed from each of [#permalink] ### Show Tags 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 Math Expert Joined: 02 Sep 2009 Posts: 46207 Re: During an experiment, some water was removed from each of [#permalink] ### Show Tags 22 Mar 2012, 11:01 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. _________________ Intern Joined: 30 Nov 2011 Posts: 29 Location: United States GMAT 1: 700 Q47 V38 GPA: 3.54 Re: During an experiment, some water was removed from each of [#permalink] ### Show Tags 22 Mar 2012, 11:27 I got u bunuel, the same percentage increase or decrease to each element in a list will not correspond to adding or subtracting the same number or constant to/from the different elements. Thanks very much. Senior Manager Joined: 13 Jan 2012 Posts: 290 Weight: 170lbs GMAT 1: 740 Q48 V42 GMAT 2: 760 Q50 V42 WE: Analyst (Other) Re: Standard Deviation question [#permalink] ### Show Tags Updated on: 16 Jun 2012, 01:44 1 Well I suppose this is actually quite easy. If you know only the basics of standard deviation, then it should be clear that if every tank loses 30% of its water, then the standard deviation also decreases by 30%. So A is sufficient, while B alone isn't as that information isn't comparable to information in the prompt. Originally posted by geometric on 16 Jun 2012, 01:20. Last edited by geometric on 16 Jun 2012, 01:44, edited 1 time in total. Intern Joined: 11 Jun 2011 Posts: 10 Re: Standard Deviation question [#permalink] ### Show Tags 16 Jun 2012, 01:42 thanks for the explanation. Was confused on the percentage part, however can you elaborate a bit on how if the percentage is changed the SD remains the same. For instance if container 1 has say 11 litres, 2 has 17, 3 has 19 30 % of each will be different 30% of higher value will be higher and for lowest value will be lowest, so SD must change isn't it?? _________________ _______________________________________________________________________________________________________________________________ If you like my solution kindly reward me with Kudos. Current Student Joined: 29 Mar 2012 Posts: 317 Location: India GMAT 1: 640 Q50 V26 GMAT 2: 660 Q50 V28 GMAT 3: 730 Q50 V38 Re: Standard Deviation question [#permalink] ### Show Tags 16 Jun 2012, 01:43 1 Hi, Standard deviation is defined as: $$\sqrt{\frac {(x_{mean}-x_1)^2+(x_{mean}-x_2)^2+...+(x_{mean}-x_n)^2}n}$$ and as you know, increasing or decreasing a each term of the series, increases/decreases the mean by same value. so,$$(x_{mean}-x_n)$$ will not change in case of addition/subtraction. But what about multiplication/division? let say each term is multiplied by "a", mean as well as each term is multiplied by a and we get: $$(ax_{mean}-ax_1)$$ Thus, standard deviation will change only in case of multiplication/division. Now back to the question; Using (1), 30% is removed, so what is left is 70% of water in tank, also, the average reduces to 70% of original. Thus new standard deviation is 70% of 10 = 7. Sufficient. Using (2), Clearly, Insufficient. Thus, Answer is (A), Regards, Manager Joined: 08 Apr 2012 Posts: 124 Re: Standard Deviation question [#permalink] ### Show Tags 16 Jun 2012, 01:46 1 1 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. _________________ Shouvik http://www.Edvento.com admin@edvento.com Director Joined: 14 Dec 2012 Posts: 810 Location: India Concentration: General Management, Operations GMAT 1: 700 Q50 V34 GPA: 3.6 Re: During an experiment, some water was removed from each of [#permalink] ### Show Tags 12 Aug 2013, 03:44 vaivish1723 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. IF WE MULTIPLY OR DIVIDE EACH ELEMENT WITH SAME FACTOR THEN RESULTANT SD is also same time multiplied or divided. we have initial SD = 10 STATEMENT 1: RESULTANT QUANTITY IN EACH TANK WILL BE 0.7 TIMES THE INITIAL VOLUME...HENCE IN SHORT WE ARE MULTIPLYING EACH TERM WITH 0.7 HENCE SD = 10*0.7 =7 HENCE SUFFICIENT STATEMENT 2:BY KNOWING AVERAGE WE CANNOT CALCULATE SD AS WE DONT KNOW HOW MUCH WATER IS TAKEN OUT FROM EACH TANK. HENCE INSUFFIECIENT. HENCE A _________________ When you want to succeed as bad as you want to breathe ...then you will be successfull.... GIVE VALUE TO OFFICIAL QUESTIONS... GMAT RCs VOCABULARY LIST: http://gmatclub.com/forum/vocabulary-list-for-gmat-reading-comprehension-155228.html learn AWA writing techniques while watching video : http://www.gmatprepnow.com/module/gmat-analytical-writing-assessment : http://www.youtube.com/watch?v=APt9ITygGss Retired Moderator Joined: 29 Oct 2013 Posts: 272 Concentration: Finance GPA: 3.7 WE: Corporate Finance (Retail Banking) Re: During an experiment, some water was removed from each of [#permalink] ### Show Tags 19 Nov 2013, 07:47 2 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. _________________ Please contact me for super inexpensive quality private tutoring My journey V46 and 750 -> http://gmatclub.com/forum/my-journey-to-46-on-verbal-750overall-171722.html#p1367876 Intern Joined: 03 Apr 2018 Posts: 8 Re: During an experiment, some water was removed from each of [#permalink] ### Show Tags 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? Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 8102 Location: Pune, India Re: During an experiment, some water was removed from each of [#permalink] ### Show Tags 22 May 2018, 07:14 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 _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: During an experiment, some water was removed from each of   [#permalink] 22 May 2018, 07:14
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# During an experiment, some water was removed from each of

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