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There are 100 employees in a company. Is the standard deviat

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There are 100 employees in a company. Is the standard deviat

by Max@Math Revolution » Wed May 23, 2018 5:02 pm

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[GMAT math practice question]

There are 100 employees in a company. Is the standard deviation of their monthly salaries less than $1000?

1) The average of the salaries is $3,000
2) The range of the salaries is $500
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Source: — Data Sufficiency |
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by Max@Math Revolution » Fri May 25, 2018 1:28 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.

Suppose d is the standard deviation of the data set and r is the range of the data set. Then d ≤ r. Since we have many variables, E is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

Conditions 1) & 2)
Since d ≤ r, we have d ≤ 500 < 1000.
Both conditions are sufficient, when taken together.

Since this question is a statistics question (one of the key question areas), CMT (Common Mistake Type) 4(A) of the VA (Variable Approach) method tells us that we should also check answers A and B.

Condition 1)
As there is no relationship between standard deviation and average, condition 1) is not sufficient.

Condition 2)
Since d ≤ r, we have d ≤ 500 < 1000.
Condition 2 is sufficient.

Therefore, B is the answer.

Answer: B
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by deloitte247 » Fri May 25, 2018 11:39 am

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The standard deviation is a measure of how far on the average the numbers in a set are from the mean.
Statement 1: The average of the salaries is $3,000, this is greater than the standard deviation of monthly salaries, statement 1 is not sufficient.
Statement 2: The range of the salaries (highest salary - lowest salary) is $500 on average their salary are relatively close together i.e standard deviation must be less than $500.
Statement 2 is sufficient
option B = answer because statement 2 alone is sufficient but statement 1 alone is not sufficient.
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