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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]

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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]

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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]

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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]

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

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New post 27 Oct 2016, 00:37
Bunuel wrote:
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.


Bunuel One question,how are we sure that one set of consecutive numbers of multiple of 7 will have 3.5 as the S.D. Can't this be the case that none of the sets of multiples of 7 will have a S.D. of 3.5?

Please help. Thanks
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Re: Let S be a finite set of consecutive multiples of 7.  [#permalink]

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New post 27 Oct 2016, 01:00
1
1
Keats wrote:
Bunuel wrote:
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.


Bunuel One question,how are we sure that one set of consecutive numbers of multiple of 7 will have 3.5 as the S.D. Can't this be the case that none of the sets of multiples of 7 will have a S.D. of 3.5?

Please help. Thanks


On the GMAT, two data sufficiency statements always provide TRUE information and these statements NEVER contradict each other or the stem. Hence if it's said that there is such a set then there must be.

FYI, ..., {0, 7}, {7, 14}, {14, 21}, {21, 28}, ... have the SD of 3.5.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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]

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Re: Let S be a finite set of consecutive multiples of 7. &nbs [#permalink] 08 Dec 2018, 02:42
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