BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

The standard deviation of the salaries of the workers in company

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 am
Location: Las Vegas, USA
Thanked: 19 times
Followed by:37 members

The standard deviation of the salaries of the workers in company

by Max@Math Revolution » Wed Apr 15, 2020 8:48 pm

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

[GMAT math practice question]

The standard deviation of the salaries of the workers in company A is \(\sqrt{5}\) and that of the workers in company B is \(\sqrt{30}\) . What is the standard deviation of the salary of company A and B’s workers together?

1) The number of workers in company A is 20 and that of company B is 30.
2) The averages of the salaries of the workers in companies A and B are the same.
Top
Source: — Data Sufficiency |
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 am
Location: Las Vegas, USA
Thanked: 19 times
Followed by:37 members

Re: The standard deviation of the salaries of the workers in company

by Max@Math Revolution » Fri Apr 17, 2020 6:54 am

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

=>

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.
Visit https://www.mathrevolution.com/gmat/lesson for details.

Since we don’t know how many workers companies A and B have, we have many variables and 0 equations, and E is most likely 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)
Let m be the average of the salaries of A and B.
Assume a1, a2, …, a20 are the salaries of the workers in A and b1, b2, …, b30 are those of the workers in B.
Since the standard deviation of the company A is \(\sqrt{5}\) , we have
[(a1-m)^2+(a2-m)^2 + … + (a20-m)^2] / 20 = 5 or (a1-m)^2+(a2-m)^2 + … + (a20-m)^2 = 100.
Since the standard deviation of the company B is \(\sqrt{30}\) , we have
[(b1-m)^2+(b2-m)^2 + … + (b30-m)^2] / 30 = 30 or (b1-m)^2+(b2-m)^2 + … + (b30-m)^2 = 900.
Then, we have
[(a1-m)^2+(a2-m)^2 + … + (a20-m)^2 + (b1-m)^2+(b2-m)^2 + … + (b30-m)^2] / 50
= (100 + 900) / (20 + 30) = 1000/50 = 20.
The standard deviation of the combined set of A and B is \(\sqrt{20}=2\sqrt{5}\) .

Since both conditions together yield a unique solution, they are sufficient.

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)
Since there is no relation between the number of data and the standard deviation, condition 1) is not sufficient.

Condition 2)
Since there is no relation between the average and the standard deviation, condition 2) is not sufficient.

Therefore, C is the answer.
Answer: C

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2) when taken together. Obviously, there may be occasions on which the answer is A, B, C, or D.
Top
Post new topic Post Reply
• Page 1 of 1