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Let S be a finite set of consecutive multiples of 7.

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Let S be a finite set of consecutive multiples of 7. [#permalink] New post 28 Jun 2013, 21:03
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Let S be a finite set of consecutive multiples of 7. How many terms are there in S?

(1) The sum of the terms in set S is 105.
(2) The standard deviation of set S is equal to 3.5
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Re: Let S be a finite set of consecutive multiples of 7. [#permalink] New post 28 Jun 2013, 21:43
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Let S be a finite set of consecutive multiples of 7. How many terms are there in S?

(1) The sum of the terms in set S is 105. Clearly insufficient. For example, consider S={28, 35, 42} and {49, 56}.

(2) The standard deviation of set S is equal to 3.5. Important property: if we add or subtract a constant to each term in a set SD will not change. From this it follows, that:

Any set with two consecutive multiples of 7 will have the same standard deviation. For example, ..., {0, 7}, {7, 14}, {14, 21}, {21, 28}, ... will have the same standard deviation.
Any set with three consecutive multiples of 7 will have the same standard deviation. For example, ..., {0, 7, 14}, {7, 14, 21}, {14, 21, 28}, {21, 28, 35}, ... will have the same standard deviation.
Any set with four consecutive multiples of 7 will have the same standard deviation. For example, ..., {0, 7, 14, 21}, {7, 14, 21, 28}, {14, 21, 28, 35}, {21, 28, 35, 42}, ... will have the same standard deviation.
...

We know the standard deviation of S is 3.5. We CAN get the standard deviations of {0, 7}, {0, 7, 14}, {0, 7, 14, 21}, ... Only one of them will have the standard deviation of 3.5. So, we can get how many terms are there in the set. Sufficient.

Answer: B.

Hope it's clear.
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Re: Let S be a finite set of consecutive multiples of 7. [#permalink] New post 29 Aug 2014, 03:49
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Re: Let S be a finite set of consecutive multiples of 7. [#permalink] New post 01 Sep 2014, 07:53
Can you post a link for tips on Standard Deviations? I'm a baby with S.D's! :/
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Re: Let S be a finite set of consecutive multiples of 7. [#permalink] New post 01 Sep 2014, 07:57
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fra wrote:
Can you post a link for tips on Standard Deviations? I'm a baby with S.D's! :/


Theory on SD: math-standard-deviation-87905.html

Check Standard Deviation Questions in our Special Questions Directory.

Hope it helps.
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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Let S be a finite set of consecutive multiples of 7.   [#permalink] 01 Sep 2014, 07:57
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