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

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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What is the standard deviation of 3 products’ prices?  [#permalink]

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18 Nov 2016, 01:24
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35% (medium)

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60% (00:57) correct 40% (01:06) wrong based on 171 sessions

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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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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

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

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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).

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

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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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26 Nov 2019, 06:07
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

The sd measures the deviation of each term from the mean.
If the terms are all the same, then the deviation is 0.

1) The sum of any two prices of these 3 products is \$1,000 sufic

3 prices: {\$500,500,500} or {\$1000,1000,0}, but \$0 is not possible since price > 0;

2) At least one of them is \$500 insufic

Ans (A)
Re: What is the standard deviation of 3 products’ prices?   [#permalink] 26 Nov 2019, 06:07
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