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Set W is made up of positive numbers. One number is removed, [#permalink]

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07 Jul 2006, 08:47

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A

B

C

D

E

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Set W is made up of positive numbers. One number is removed, and the remaining numbers comprise set V. Is the mean of the numbers in V equal to the mean of the numbers in W?

(1) All numbers in W are integers.
(2) The mean of the numbers in W is 17.5.

I know it is not (A). I am pretty confident it is not (B). (Just pick 3 numbers for W with average 17.5 and experiment with removing one. There infinite number of possibilities.)

I know it is not (A). I am pretty confident it is not (B). (Just pick 3 numbers for W with average 17.5 and experiment with removing one. There infinite number of possibilities.)

I - insufficient - Ifall no.s are same, then mean can be same.. or if no.s are different, then anything is possible.

II. insufficient - mean is 17.5.. it may be possible to have all no.s as 17.5, which would yield same mean for V/W .. or no.s can be differnet, yielding to dif. mean.

Combining,
we know that no.s are integers and not all integers are same .. So, If we remove one integer from the set, it shd yield a diff. mean

Combining, we know that no.s are integers and not all integers are same .. So, If we remove one integer from the set, it shd yield a diff. mean

Still not convinced this proves it. What if you find a set with all but one integers the same that yields 17.5 as average? If you remove any one number from (assuming there more than 3 numbers in the set) the set the median would not change. Is it true that there would be no combination that can give you mean of 17.5 again? Hard to believe, there are so many numbers out there...

Combining, we know that no.s are integers and not all integers are same .. So, If we remove one integer from the set, it shd yield a diff. mean

Still not convinced this proves it. What if you find a set with all but one integers the same that yields 17.5 as average? If you remove any one number from (assuming there more than 3 numbers in the set) the set the median would not change. Is it true that there would be no combination that can give you mean of 17.5 again? Hard to believe, there are so many numbers out there...

sorry guys. i was rushing to guess B thinking that all numbers in set w are integers. it should be C.

we know from 1 and 2 that w has all integers and the number of integers is even. for ex: 10, 15, 20, 25. the sum is 70 and avg = 17.5. if we take out one integer, the avg of the remaining integers wont be the same. it is only possible with numbers.

I - insufficient - Ifall no.s are same, then mean can be same.. or if no.s are different, then anything is possible.

II. insufficient - mean is 17.5.. it may be possible to have all no.s as 17.5, which would yield same mean for V/W .. or no.s can be differnet, yielding to dif. mean.

Combining, we know that no.s are integers and not all integers are same .. So, If we remove one integer from the set, it shd yield a diff. mean

Aren't you assuming that all the integers are different ?? As I understand, unelss mentioned that all integers are different,we have consider a situation where they could be same..