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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42 GPA: 3.82
If the average (arithmetic mean) of 100 numbers is 50, what is the sta  [#permalink]

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[GMAT math practice question]

If the average (arithmetic mean) of 100 numbers is 50, what is the standard deviation of the numbers?

1) The smallest number is 50
2) The largest number is 50

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Re: If the average (arithmetic mean) of 100 numbers is 50, what is the sta  [#permalink]

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MathRevolution wrote:
[GMAT math practice question]

If the average (arithmetic mean) of 100 numbers is 50, what is the standard deviation of the numbers?

1) The smallest number is 50
2) The largest number is 50

Question : what is the standard deviation of the numbers?

Statement 1: The smallest number is 50

If the smallest number is equal to 50 which is Mean then every term should be equal to mean only

And since all the terms of the set are equal to 50 hence there Standard deviation of the set = 0

SUFFICIENT

Statement 2: The Largest number is 50

If the Largest number is equal to 50 which is Mean then every term in the set should be equal to mean only

And since all the terms of the set are equal to 50 hence there Standard deviation of the set = 0

SUFFICIENT

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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8029
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: If the average (arithmetic mean) of 100 numbers is 50, what is the sta  [#permalink]

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1
=>
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 VA(Variable Approach) method is modifying the original condition and the question, and rechecking the number of variables and the number of equations. We often encounter this type of question in the GMAT quant exam these days. If the mean is equal to either the maximum or the minimum, or the range ( = Max – Min ) is zero, then the standard deviation is zero.

Condition 1)
All data items are greater than or equal to 50, and their average is 50.
It means that all data items are equal to 50.
Since all of the data items are equal, their standard deviation is 0.
This is sufficient.

Condition 2)
All data items are less than or equal to 50, and their average is 50.
It means that all data items are equal to 50.
Since all of the data items are equal, their standard deviation is 0.
This is sufficient too.

Therefore, the answer is D.

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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Re: If the average (arithmetic mean) of 100 numbers is 50, what is the sta  [#permalink]

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_________________ Re: If the average (arithmetic mean) of 100 numbers is 50, what is the sta   [#permalink] 23 Jul 2019, 05:07
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