mgmat advance quant book doubt

[ArchitG318]

Hi ron/stacey
Following is question from Mgmat Advance quant (workout set 6 ,q59 ) please help.

Set M contains seven integers and set N contains three values chosen from set M. Is the standard deviation of Set N greater than the standard deviation of set M?
1) Set N contains the median of set M.
2) The range of set M and set N are equal .

OA is B.
I think that answer should be E as it is not specified that SET M has distinct integers. If the set M has same integers then SD would be equal of both sets .
Correct me ...

[RonPurewal]

hi,
can you please reproduce the answer key?
...because this problem as written most certainly does NOT have answer B.

your objection is valid—but, in fact, you don't even need to go there. statement 2 can be proved insufficient even if all 7 integers are different.

e.g.,

M = {1, 2, 3, 50, 97, 98, 99}
N = {1, 50, 99}
here, to get N we remove four values that are all 'extreme' (2, 3, 97, and 98). thus N will clearly have a smaller SD.

M = {1, 48, 49, 50, 51, 52, 99}
N = {1, 50, 99}
here, to get N we remove four values that are very very close to the center. thus N will have a substantially larger SD, because the effect of '1' and '99' will be much more pronounced with the middling values gone.

[RonPurewal]

...and actually those 2 cases prove that the answer is E, since both of them also satisfy statement 1.

so now i'm really interested in seeing this answer key. how does it (supposedly) show that statement 2 is sufficient?

[ArchitG318]

...and actually those 2 cases prove that the answer is E, since both of them also satisfy statement 1.

so now i'm really interested in seeing this answer key. how does it (supposedly) show that statement 2 is sufficient?

Yup i guess they did a mistake of considering only one case.
Here is the solution written.
" Standard deviation is a measure of the spread of a group of numbers.

1) INSUFFICIENT: If set M contains { 1,2,3,4,5,6,7}, then 4 is the median. Set N could be {3,4,5}, which has a smaller standard deviation than set M because the two sets have the same average but N is not as spread out as M .
Alternatively, N could be {1,4,7} which has larger standard deviation than set M because the two sets still have the same average , but N is now more spread out than N . (It doesn't have additional values that are closer to the average )

2) SUFFICIENT : if set M contains the numbers {1,2,3,4,5,6,7} and set n has the same range , then N must contain 1 and 7 . if set N contains {1,4,7} then N has a larger SD than M . if set N contains {1,2,7} the standard deviation actually increases even more ( because the numbers are no longer evenly distributed). No matter what combination you try, the standard deviation of N has to be greater than SD of M.
The correct answer B
............................................

Also, Ron these workout sets are of 700+ level questions please through some light on as to how much time should i take solving each set of 10 questions.
Currently I am taking 25-30 mins . (more time when a problem of sequence is there requiring cases to be written down and adding the terms( no formula could be applied) ; and geometry problems which requires a lot of visualization ( again where no formula could be applied ).
So i guess these problems are meant to take 3 mins .
So, i was wondering then in real gmat as the level increases time might turn out to be a constraint.
Currently, I am scoring q48 in gmat prep consistently(no time issues ). Curious to know how to make it to q51.

I know the question is very broad and vague . But if u could answer it somehow might turn out to be helpful for me .

[tim]

Good catch. After looking at the question and answer in the book, it looks like the intent was to indicate that M consisted of seven consecutive integers, but the word "consecutive" got left off. I will submit this to be added to our errata list.

To address your other question, 25-30 minutes is reasonable for a set of ten questions this difficult. Just remember that you're going to have to buy that time back from somewhere else - either by skipping a problem occasionally or, preferably, by moving faster on the easier problems.

[RonPurewal]

So i guess these problems are meant to take 3 mins .
So, i was wondering then in real gmat as the level increases time might turn out to be a constraint.

'hard' problems are not, to any statistically significant extent, longer than other problems.
to see this, just flip through the OG, in which the problems are listed in (very rough) 'difficulty' order. as you move forward, do the problems get longer? nope.

[RonPurewal]

MORE IMPORTANTLY,
good time management has nothing to do with counting minutes and seconds.

good time management consists of recognizing when you've stopped making progress, and IMMEDIATELY transitioning to something else at that point.
'something else' could be the next problem, or it could be a different approach to the same problem. it just needs to be ... well... something else.

if you have this habit, then you shouldn't need to look at the timer more than a couple times per section—perhaps at quarter-intervals (problems #10, #19, #28) or at thirds (problems #13 and #25).
... and even at those points, you shouldn't NEED to check the clock; these 'checkpoints' should be more of a formality than anything else.

in other words, checking the timer is like double-checking your door locks before you go on a trip: unnecessary, but good for reassurance.
technically it should be unnecessary to check the door locks, because you should be locking the doors simply as a good habit. but it's still nice to have the extra feeling of security that comes from double-checking them.
similarly, you shouldn't find it necessary to check the timer, because, if you have good time-management habits, you should be finishing this stuff on time anyway.