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The data set X has 6 elements. Its mean is 0 and its standar

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The data set X has 6 elements. Its mean is 0 and its standar

by Max@Math Revolution » Tue Jun 25, 2019 11:52 pm

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[GMAT math practice question]

The data set X has 6 elements. Its mean is 0 and its standard deviation is d, where d is not zero. When we add a new data element x to the set X, D is the standard deviation of the new set of 7 elements. Is D < d?

1) |x| < d
2) x = 0
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Source: — Data Sufficiency |
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by Max@Math Revolution » Fri Jun 28, 2019 12:32 am

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Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary.

Set X={a1, a2, ......, a6}, mean=0 and standard deviation=d. The new set = {a1, a2, ......, a6, x} has standard deviation D. Recall that the standard deviation reflects the distance between each element of the data set and the data set's average,

Conditions 1)
Since the distance between x and the mean of the set X is less than d, the standard deviation D of the new set is less than d.
Thus, condition 1) is sufficient.

Condition 2)
Since the distance between 0 and the mean of the set X is less than d, the standard deviation D of the new set is less than d.
Thus condition 2) is sufficient.

Therefore, D is the answer.
Answer: D

This question is a CMT4(B) question: condition 2) is easy to work with and condition 1) is difficult to work with. For CMT4(B) questions, D is most likely to be the answer.
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by deloitte247 » Thu Jul 04, 2019 5:49 am

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Standard deviation reflects the distance between each elements of the data set and the data set's average.
$$Data\ set\ x=a1,\ a2,\ ...,\ a6\ where\ deviation=d.$$
$$New\ data\ set\ x=a1,\ a2,\ ...,\ a6\ where\ deviation=D.$$
Now the question is to find if D < d.
Statement 1=> /x/ < d
This means that the distance between 'x' and the mean of the set 'x' is less than 'd'.
Therefore, 'D' will be less than 'd'. Hence, statement 1 is SUFFICIENT

Statement 2 => x = 0
This means that the distance between 0 and the mean of set 'x' is less than 'd'. Hence, 'D' is less than 'd'. Therefore, statement 2 is SUFFICIENT.

Both statement alone are SUFFICIENT.
Answer = Option D
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