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

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.



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




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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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
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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%.
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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.
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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.

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),

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

I) For each tanks, 30% of the volume of water that was in the tank at the beginning of the experiment was removed during the experiment.

II) The average(AM) of the volumes of the water in the tanks at the end of the experiment was 63 gallons.

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.

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