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 [#permalink] New post 17 Feb 2007, 12:40
Is there a short version to this problem without listing numbers for the sets and trying out different numbers?

S is a set containing 9 different numbers. T is a set containing 8 different numbers, all of which are members of S. Which of the following statements CANNOT be true?

A) The mean of S is equal to the mean of T
B) the median of S is equal to the median of T
C) the range of S is equal to the range of T
D) The mean of S is greater than the mean of T
E) The range of S is less than the range of T
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Re: 987*987 [#permalink] New post 17 Feb 2007, 13:46
hobbit wrote:
ggarr wrote:
Here's one
What is 987 * 987?


with no options to choose from it is hard to show some important shortcuts that can be made (like rough estimation digit checking etc...)
we are left with pure computation.... and the worst thing you can do is to write it down and do paper&pencil long multiplication....

here is what i do:
987=1000-13
use the formula (a-b)^2= a^2-2ab+b^2
1000^2 is 1M
13^2 is 169
and 2*13*1000=26000
so the answer is 974,169
Here it is with options.

What is 987*987?
A)974,169
B)974,219
C)974,549
D)975,019
E)975,369
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 [#permalink] New post 20 Feb 2007, 14:19
umuhanga wrote:
Is there a short version to this problem without listing numbers for the sets and trying out different numbers?

S is a set containing 9 different numbers. T is a set containing 8 different numbers, all of which are members of S. Which of the following statements CANNOT be true?

A) The mean of S is equal to the mean of T
B) the median of S is equal to the median of T
C) the range of S is equal to the range of T
D) The mean of S is greater than the mean of T
E) The range of S is less than the range of T


i wouldn't even think of trying out numbers....
this kind of question test the understanding of the concept of mean,range and median and their behavior. so basic understanding is enough here. here are the explanations:
we should remember that S is exactly like T plus one number which is different.
a) is there a possibility to add a number to a set that will keep the mean unchanged? of course there is... you can add the mean itself.
b) is it possible to add a number to a set of 8 numbers so that the median will remain the same? yes of course... the median of an even number of data points is half the sum of the middle points. adding this "half the sum of middle points" to the set creates another set with the same median.
c) is there a possibility to to add a number to a set without changing the range? sure there is, just add a number which is between the minimum and the maximum.
d) is there a possibility to add a number to a set so that the average increase? sure there is, just add a big number.
e) can you add a number to a set so that the range will decrease? oh no... if you add a number, either the range remains the same if you added something that is between the min and the max, or increase if you add something above the max or below the min.

E is your answer.
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Re: 987*987 [#permalink] New post 20 Feb 2007, 14:21
ggarr wrote:
hobbit wrote:
ggarr wrote:
Here's one
What is 987 * 987?


with no options to choose from it is hard to show some important shortcuts that can be made (like rough estimation digit checking etc...)
we are left with pure computation.... and the worst thing you can do is to write it down and do paper&pencil long multiplication....

here is what i do:
987=1000-13
use the formula (a-b)^2= a^2-2ab+b^2
1000^2 is 1M
13^2 is 169
and 2*13*1000=26000
so the answer is 974,169
Here it is with options.

What is 987*987?
A)974,169
B)974,219
C)974,549
D)975,019
E)975,369


with these options, just do the computation. the options are too similar to eachother to make estimations.
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Re: [#permalink] New post 11 Jan 2010, 08:30
yogeshsheth wrote:
Some Tips on Standard Deviation Sums particularly DS
1) If you add or subtract a particular constant from all the terms the sd deviation remains same and the mean is either increased or decreased by constant
2) If you multiply all terms by x then SD =x times old SD and mean = x times old mean.
Quote:
3) For comparing the SD for two sets any information about mean ,median,mode and range are insufficient unless you can determine the individual terms from the given data.


you meant here to know number of terms ?

SD of 28 consecutive number is same picked from any where, so in this case knowing number of elements is enough . Am i wrong in this approach?this is what the point 1 says in fact.

Quote:
Hope these help


Cheers
Yogesh
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Re: TIME SAVING PROJECT [#permalink] New post 26 Jul 2014, 07:22
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