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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.

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

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27 Oct 2016, 01:37

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?

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.
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