List S and list T each contain 5 positive integers, and for each list

Question

List S and list T each contain 5 positive integers, and for each list the average (arithmetic mean) of the integers in the list is 40. If the integers 30, 40, and 50 are in both lists, is the standard deviation of the integers in list S greater than the standard deviation of the integers in list T ?

(1) The integer 25 is in list S.
(2) The integer 45 is in list T.

Bunuel · Accepted Answer

List S and List T each contain 5 positive integers, and for each list the average (arithmetic mean) of the integers in the list is 40. If the integers 30,40,50 are in both lists, is the standard deviation of the integers in list S greater than the standard deviation of the integers in list T?

(1) The integer 25 is in list S
(2) The integer 45 is in list T

The mean of 5 integers is 40 means that the sum of these 5 integers is 5*40=200. The sum of the 3 out of these 5 integers is 30+40+50=120, thus the sum of the remaining 2 integers in each lists is 200-120=80.

(1) The integer 25 is in list S. The 5th integer in S is 80-25=55. We know list S. Not sufficient.
(2) The integer 45 is in list T. The 5th integer in T is 80-45=35. We know list T. Not sufficient.

(1)+(2) We know all terms of each set, thus we can get the standard deviation of each and compare. Sufficient.

Answer: C.

As for your question:

S = {25, 30, 40, 50, 55}
T = {30, 35, 40, 45, 50}

The standard deviation of a set shows how much variation there is from the mean, how widespread a given set is. So, a low standard deviation indicates that the data points tend to be very close to the mean, whereas high standard deviation indicates that the data are spread out over a large range of values.

List T is less widespread thus will have lower standard deviation than that of list S.

Hope it's clear.

jsnooky33 · Answer

I'm going with C here.

1) and 2) both give values for s and t, respectively. To keep the average at 40, we are able to guess the final unknown values in the set.

T = {30, 35, 40, 45, 50}
S = {25, 30, 40, 50, 55}

There is a greater range with S, thereby showing it has a higher standard deviation.

paddyboy · Answer

Yep - C.

1) Calculate all members of S, but not of T. Insuff.
2) Calculate all members of T, but not of S. Insuff.

Combine. We have both sets and can get a result.

GMATT73 · Answer

Straightforward (C). If we know the (arithmetic) mean, then we can easily solve for the missing number in each list by using the average formula. 

Compare averages in each set to determine the SD.

fozzzy · Answer

Just curious when the statements are combined

The S.D of Set S will be greater than S.D of set T?

No doubt the answer is C

LogicGuru1 · Answer

Using stimulus we know 
S={30,40,50,-,-,} two unknown ; Mean is 40
T={30,40,50,-,-} two unknown ; Mean is 40

Lets use the quick "EYEBALL SD FROM MEAN" method .
Now the set which will have values far from 40 will have a greater SD

Stament(1) The integer 25 is in list S
It means our set is now complete S={25,30,40,50,55} 
But it tells us nothing about element of other set.
INSUFFICIENT

(2) The integer 45 is in list T
Meaning now out set T is complete t={30,35,40,45,50}
But it tells that nothing about element of set S
INSUFFICIENT

MERGING BOTH 
S={25,30,40,50,55} 
T={30,35,40,45,50}

Lets use the quick "EYEBALL SD FROM MEAN" method .
SD of S will be greater since it extreme values are more spread out from the mean (40-25 =15 and 40-55=-15) Exact SD will be 12.7
SD of T will be lower since it extreme values are less spread out from the mean (40-30 =10 and 40-50=-10) Exact SD will be 7.9

ANSWER IS C

GulfTube · Answer

i) one value in S is 25 so other is 55
T can have 40,40 in which case Yes
T can have 20, 60 in which case No
insufficient

ii) similar two cases can be build. insufficient

together: S: {25, 30, 40, 50, 55} T: {30, 35, 40, 45, 50} clearly Yes Sufficient  C

List S and list T each contain 5 positive integers, and for each list

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

GMAT Data Sufficiency (DS) Questions

List S and list T each contain 5 positive integers, and for each list

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia