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A and B are subsets of positive integers. Are the standard deviations of A and B equal?

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A and B are subsets of positive integers. Are the standard deviations of A and B equal?

by Max@Math Revolution » Wed Mar 04, 2020 12:12 am

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[GMAT math practice question]

A and B are subsets of positive integers. Are the standard deviations of A and B equal?

1) A is the set of all odd numbers between 1 and 100, inclusively.
2) B is the set of all even numbers between 1 and 100, inclusively.
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Source: — Data Sufficiency |
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Re: A and B are subsets of positive integers. Are the standard deviations of A and B equal?

by Max@Math Revolution » Fri Mar 06, 2020 1:57 am

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B

C

D

E

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Since we have 2 variables (A and B) and 0 equations, C 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)

B = { 2, 4, 6, … , 100 } = A + 1 = { 1, 3, 5, … , 99 } + 1.
Since set B is the shift of set A by 1, sets A and B have the same standard deviation.

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 condition 1) does not have any information regarding set B, it is not sufficient obviously.

Condition 2)

Since condition 2) does not have any information regarding set A, it is not sufficient obviously.

Therefore, C is the answer.
Answer: C

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B, or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D, or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
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