Data Sufficiency

ziyuenlau wrote:A study involved a total of 6 barrels of a liquid mixture. If the standard deviation of the volume of liquid in the barrels was 10 liters at the start of the study, what was the standard deviation of the volumes of liquid in the barrels at the end of the study?

(1) At the start of the study, the researchers were required to remove 30% from each of the volumes of liquid mixture.

(2) The average (arithmetic mean) volume of liquid mixture in the barrels at the end of the study was 63 liters.

Hi ziyuenlau,

This question is awkwardly worded and thus very confusing. I recall a GMATprep question on the similar lines.

All it wants to convey is following:

A study involves a total of 6 barrels filled with liquid. If the standard deviation of the volumes of liquid in the barrels was 10 liters at the start of the study, what was the standard deviation of the volumes of liquid in the barrels at the end of the study?

We have 6 barrels that are filled with liquid. The volumes in the barrels may or may not be equal. Since we are given SD of volumes = 10 liters, it implies that the volumes in all the barrels in not equal.

Had the volumes in the barrels been equal, SD would have been 0. No deviation in volumes at all.

Two things to note in the case of SD.

1. If a constant is added to/subtracted from each of the elements of a set, SD remains unchanged, while arithmetic mean increases/decreases by the value of the constant.

Say Set A is: {1, 2, 3, 4, 5}, SD = x (computation of SD is beyod the scope of the GMAT) and Arithmetic mean = 3.

Say a constant '5' is added to each of the elements of set A

Thus, Set B = {6, 7, 8, 9, 10}, SD = x (unchanged) and Arithmetic mean = 3+5 = 8.

2. If a constant is multiplied/divided to each of the elements of a set, SD, as well as, arithmetic mean is multiplied/divided by the value of the constant.

Say Set A is: {1, 2, 3, 4, 5}, SD = x and Arithmetic mean = 3.

Say a constant '5' is multiplied to each of the elements of set A,

Thus, Set B = {5, 10, 15, 20, 25}, SD = 5x (Changed; multiplied by 5) and Arithmetic mean = 3*5 = 15.

Coming back to the question...

S1: At the start of the study, the researchers were required to remove 30% from each of the volumes of liquid mixture.

I think it should be worded as: During the study, the researchers removed 30% of liquid from each of the 6 barrels.

Removal of 30% means that if a barrel had x liters of liquid, it has x*(1-30%) = x*0.7 = 0.7x liters now.

This is a case of multiplying each element by a constant '0.7'.

As discussed in Case 2, we see that SD would get multiplied by 0.7, thus SD at the and of the study = Old SD * 0.7 = 10*0.7 = 7 liters--Sufficient.

Let's take statement 2

S2: The average (arithmetic mean) volume of liquid mixture in the barrels at the end of the study was 63 liters.

Since we do not know how much each barrel contained before the start of the study, we cannot calculate SD after the study. Insufficient.

The correct answer: A

Hope this helps!

Relevant book: Manhattan Review GMAT Sets & Statistics Guide

-Jay
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