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

Question

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

Bunuel · Accepted Answer

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.

fra · Answer

Can you post a link for tips on Standard Deviations? I'm a baby with S.D's! :/

Bunuel · Answer

Theory on SD: math-standard-deviation-87905.html Check Standard Deviation Questions in our Special Questions Directory . Hope it helps.

keats · Answer

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

Bunuel · Answer

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.

Debashis Roy · Answer

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).

Thanks in advance

Bunuel · Answer

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

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GMAT Data Sufficiency (DS) Questions

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

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