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Let S be a finite set of consecutive multiples of 7.  [#permalink]

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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
Math Expert V
Joined: 02 Sep 2009
Posts: 62448
Re: Let S be a finite set of consecutive multiples of 7.  [#permalink]

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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.

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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Can you post a link for tips on Standard Deviations? I'm a baby with S.D's! :/
Math Expert V
Joined: 02 Sep 2009
Posts: 62448
Re: Let S be a finite set of consecutive multiples of 7.  [#permalink]

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

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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.

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?

Math Expert V
Joined: 02 Sep 2009
Posts: 62448
Re: Let S be a finite set of consecutive multiples of 7.  [#permalink]

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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.

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?

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

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Bunuel
cant this be the case that sets consisting of different numbers of consecutive multiples of 7 can still have the same SD as 3.5? For example a set of 3 consecutive multiples of 7 has SD=3.5 and so has another set consisting of may be 4 or 2 consecutive multiples of 7(more spread out bothways).

Math Expert V
Joined: 02 Sep 2009
Posts: 62448
Re: Let S be a finite set of consecutive multiples of 7.  [#permalink]

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Debashis Roy wrote:
Bunuel
cant this be the case that sets consisting of different numbers of consecutive multiples of 7 can still have the same SD as 3.5? For example a set of 3 consecutive multiples of 7 has SD=3.5 and so has another set consisting of may be 4 or 2 consecutive multiples of 7(more spread out bothways).

No.

More elements you add to a set of consecutive multiples, more widespread it becomes, thus larger SD you get. For example:

The standard deviation of {0, 7} = 3.5
The standard deviation of {0, 7, 14} = ~5,7
The standard deviation of {0, 7, 14, 21} = ~7.8
The standard deviation of {0, 7, 14, 21, 28} = ~9.9
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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.   [#permalink] 03 Jan 2020, 01:44
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