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Note: Range Rule of Determining SD states that the SD of a set is equal to 1/4 of its range.

(1) Set A consists of consecutive multiples of 10
No information about set B.
(Insufficient)

(2) Set B consists of consecutive multiples of 2
No information about set A.
(Insufficient)

Statement 1&2 together:

Case 1:
Let Set A = {10,20,30,40}
Set B = {10,20,30,40}
S.D. will be equal.

Case 2: SET A = {10,20,30,40}
Range = 40-10 = 30
SD = 30/4 = 7.5

Set B = {2,8,14,20,26,32,38}
Range = 38-2 = 36
SD = 36/4 = 9

SD of Set B is greater

Case 3: SET A = {10,20,30,40}
Range = 40-10 = 30
SD = 30/4 = 7.5

Set B = {2,8,14,20}
Range = 20-2 = 18
SD = 18/4 = 4.5

SD of Set A is greater

(Insufficient)

IMO E

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In theory, the standard deviation of either set could be zero if one of the sets contains only one element. If we allow that possibility, the answer is immediately E.

If we disallow that possibility, then if the set of consecutive multiples of 10 is {10, 20}, its standard deviation is 5 (every element in the set is 5 away from the mean, so that is automatically the standard deviation). If you take a very large set of consecutive multiples of 2, say all the multiples of 2 between 0 and 1000, almost every value in this set will be more than 5 away from the mean, and the standard deviation will be much larger than 5. So the answer is still E.

If we knew the sets were the same size, then both statements would be sufficient together, since then the elements of A would be a greater distance apart than the elements of B (in fact, the standard deviation of A would be precisely five times as big as that of B, because the distances within A would be five times as big).
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Ans - E

Standard deviations is under root of variance, which is diff of term and the av, the more this deviation is the more is SD

Statement 1
Given info on set A, but no B. Not sufficient

Statement B
Gives info on set B, but no A, Not sufficient

With Statement 1 and 2
Even if Set A is consecutive multiple of 10, and set B is consecutive multiple of 2.

It is unsure what would the variance be depending of the starting number. Set B can still be a multiple of set A, which will prove otherwise.

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Standard deviation depends on the variance and also number of terms in the set.Here in both the statements we don't have number of terms mentioned so we can't conclude from any of the statements.

Answer E
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Bunuel

Competition Mode Question



Is the standard deviation of set A is greater than standard deviation of set B ?

(1) Set A consists of consecutive multiples of 10
(2) Set B consists of consecutive multiples of 2

Someone just pointed out I missed the word consecutive twice!
I subsequently change my answer to Ian's above: https://gmatclub.com/forum/is-the-stand ... l#p2561705
:)
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BrentGMATPrepNow
Bunuel

Competition Mode Question



Is the standard deviation of set A is greater than standard deviation of set B ?

(1) Set A consists of consecutive multiples of 10
(2) Set B consists of consecutive multiples of 2
Target question: Is the standard deviation of set A is greater than standard deviation of set B ?

When I scan the two statements, they both feel insufficient, AND I’m pretty sure I can identify some cases with conflicting answers to the target question. So, I’m going to head straight to……

Statements 1 and 2 combined
There are several scenarios that satisfy BOTH statements. Here are two:
Case a: Set A = {10, 20, 30, 40} and Set B = {2, 2, 2, 2}. In this case, the answer to the target question is YES, the standard deviation of set A is greater than standard deviation of set B
Case b: Set A = {11, 11, 11, 11} and Set B = {2, 20, 200, 2000}. In this case, the answer to the target question is NO, the standard deviation of set A is NOT greater than standard deviation of set B
Since we can’t answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Hi BrentGMATPrepNow

Can you please share some clarifications on the highlighted examples. Shouldn't the numbers be consecutive multiples of 10 and 2 respectively.

Also - Can we just conclude that the information combined is not sufficient as the number of terms are not known in either of the sets ?
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gmatophobia
Can you please share some clarifications on the highlighted examples. Shouldn't the numbers be consecutive multiples of 10 and 2 respectively.
Also - Can we just conclude that the information combined is not sufficient as the number of terms are not known in either of the sets ?

Thanks for the heads up!
I've changed my solution accordingly.

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Quantity A = The standard deviation of the set {1, 3, 5}

Quantity B = The standard deviation of the set {8,10,12}

Quantity A is greater.Quantity B is greater.The two quantities are equalThe relationship cannot be determined from the information given.
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