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On a side note, when a question tells you a set S has numbers x,y,z - do we assume that x y z will always be different numbers? or can they be the same number, but repeated 3 times.

On a side note, when a question tells you a set S has numbers x,y,z - do we assume that x y z will always be different numbers? or can they be the same number, but repeated 3 times.

1: Not enough as all members can be same in that case SD is 0 which is not +ve but in other case when all numbers are +ve and different SD will be +ve hence insufficient. 2: Enough as SD is zero which is not +ve hence suffcient.

I'm not going to go into "how to solve" since many others are do it much better than I do.

I think for this question the key factors to know are: 1) definition of standard definition 2) definition of "0"

remember, when all numbers are the same or if there is one number in the set, the standard deviation is 0. 0 is not a positive integer. (positive integer is > 0).

Sorry but is there some mistake here. Thought this helpful set of Bunuel

Did you type correctly? Y should be T, correct? "Set T consists of odd integers divisible by 5" and "T consists of only one member" in statement 2 are also inconsistant.

1: Anyway, statement 1 is not helpful in finding SD. 2: Statement 2 is definitely helps to get the SD, which is 0 in this case as the SD of an element is 0.

bigfernhead wrote:

Set Y consists of odd integers divisible by 5. Is standard deviation of T positive?

1) All members of T are positive 2) T consists of only one member

On a side note, when a question tells you a set S has numbers x,y,z - do we assume that x y z will always be different numbers? or can they be the same number, but repeated 3 times.

For your side question, can you post the question if you have? Because a question with context would be very useful in anylizing the issue on hand.

IMO, real gmat test do not offer such a confused context.
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Notice how X and Y even though different variables, can take on the same value (both x and y = 4), as per the OE in the post. I'm wondering if this is can be the case in the real GMAT.

Did you type correctly? Y should be T, correct? "Set T consists of odd integers divisible by 5" and "T consists of only one member" in statement 2 are also inconsistant.

1: Anyway, statement 1 is not helpful in finding SD. 2: Statement 2 is definitely helps to get the SD, which is 0 in this case as the SD of an element is 0.

bigfernhead wrote:

Set Y consists of odd integers divisible by 5. Is standard deviation of T positive?

1) All members of T are positive 2) T consists of only one member

On a side note, when a question tells you a set S has numbers x,y,z - do we assume that x y z will always be different numbers? or can they be the same number, but repeated 3 times.

For your side question, can you post the question if you have? Because a question with context would be very useful in anylizing the issue on hand.

IMO, real gmat test do not offer such a confused context.

(1) 1: SD = 0; 1, 15, 15: SD = some +ve value............Insuff (2) -15: SD = 0; 15: SD = 0 as well. In all cases, for any single digit, SD = 0 - NOT positive. Hence, B
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The question is if it's positive or not. From both the statements we can make out if its positive or not. Stat 1: always +ve Stat 2: always 0 - Not positive. So we can conclude both the statements alone are suffice. option D, Please let me know if im wrong.

(1) 1: SD = 0; 1, 15, 15: SD = some +ve value............Insuff (2) -15: SD = 0; 15: SD = 0 as well. In all cases, for any single digit, SD = 0 - NOT positive. Hence, B

> odd integers divisible by 5 are 5,15,25,35,45 mean = 25 S.D = ((20^2 + 10^2 + 0^2 + 10^2 + 20^2) /5)^(1/2) which is always positive.

case 2. say -5,-15,25,35,45 mean = 13 S.D = +ve in any case.

S1 is not sufficient. Consider Set T consisting of the same number elements ([4, 4, 4], for example). Then SD = 0. You can see more details in this post above: ds-stds-m08q09-73347.html?view-post=709035#p709035

kalrac wrote:

The question is if it's positive or not. From both the statements we can make out if its positive or not. Stat 1: always +ve Stat 2: always 0 - Not positive. So we can conclude both the statements alone are suffice. option D, Please let me know if im wrong.

The answer is B. (1) is insufficient as we don't know if all elements are same or different. (2) says there is only 1 element, so SD = 0, which is a definitive answer.
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Statement 1 : All members of T are positive We have two possibilities here

Case a) all the members are same => e.g T= {5,5,5} = {5} (Since by definition a 'Set' is a unique collection of objects.) => S.D = 0

Case b) all the members are different => e.g. T = {5,15,25} => S.D. = some positive number.

Since statement 1 is giving two possibilities , its Not Sufficient

Statement 2 : Set T consists of only one member => Since its only one member , S.D. =0 Hence Statement 2 is Sufficient

Hence the Answer is B

Best answer to a tricky question! Fell into the trap and didn't consider the difference between 'positive' and positive or null'... This one goes on my error log.
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