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What is the standard deviation of 3 products’ prices?

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What is the standard deviation of 3 products’ prices?  [#permalink]

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New post 18 Nov 2016, 01:24
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What is the standard deviation of 3 products’ prices?

1) The sum of any two prices of these 3 products is $1,000
2) At least one of them is $500

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Re: What is the standard deviation of 3 products’ prices?  [#permalink]

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New post 18 Nov 2016, 06:41
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MathRevolution wrote:
What is the standard deviation of 3 products’ prices?

1) The sum of any two prices of these 3 products is $1,000
2) At least one of them is $500


Target question: What is the standard deviation of 3 products’ prices?

NOTE: With questions involving standard deviation, the test-makers often like to test our knowledge of the fact that, if all of the values in a set are EQUAL, then the standard deviation of that set is ZERO.

Statement 1: The sum of any two prices of these 3 products is $1,000
This tells us that the price of EACH product is $500
In other words, the 3 prices must be $500, $500 and $500
Since all 3 values are equal, the standard deviation of 3 products’ prices is ZERO
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: At least one of them is $500
There are several possible scenarios that satisfy statement 2. Here are two:
Case a: the prices are $500, $500 and $500, in which case the standard deviation of 3 products’ prices is ZERO
Case b: the prices are $1, $500 and $1,000,000, in which case the standard deviation of 3 products’ prices is NOT zero
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer:

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Re: What is the standard deviation of 3 products’ prices?  [#permalink]

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New post 21 Nov 2016, 02:00
==> In the original condition, there are 3 variables. Therefore, E is most likely to be the answer. For con 1), the sum of any 2 prices of the products is always 1,000, so if you add the three equations a+b=1,000, b+c=1,000, and c+a=1,000 together, you get 2(a+b+c)=3,000 and a+b+c=1,500 each, and using substitution, a=b=c=500. Thus, the standard deviation is 0, hence it is sufficient. Therefore, the answer is A. This question is CMT 4 (A).

Answer: A
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Re: What is the standard deviation of 3 products’ prices?  [#permalink]

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New post 06 Dec 2016, 15:46
MathRevolution wrote:
What is the standard deviation of 3 products’ prices?

1) The sum of any two prices of these 3 products is $1,000
2) At least one of them is $500


woah..took me 17 seconds to answer :D

2 clearly is not sufficient.

1. basically tells us that the prices are equal, meaning only one thing - SD is equal to zero
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Re: What is the standard deviation of 3 products’ prices?  [#permalink]

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Re: What is the standard deviation of 3 products’ prices?   [#permalink] 01 Oct 2018, 04:17
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