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What is the median value of the set R, if for every term in

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What is the median value of the set R, if for every term in [#permalink] New post 07 May 2013, 04:27
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What is the median value of the set R, if for every term in the set, Rn = Rn–1 + 3?

(1) The first term of set R is 15.
(2) The mean of set R is 36.
[Reveal] Spoiler: OA

Last edited by Bunuel on 08 May 2013, 05:10, edited 1 time in total.
Renamed the topic and edited the question.
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Re: medians [#permalink] New post 07 May 2013, 05:38
rochak22 wrote:
8. What is the median value of the set R, if for every term in the set, Rn = Rn–1 + 3?
(1) The first term of set R is 15. (2) The mean of set R is 36.


1. Doesn't say anything about the how many elements are in the set. Insuff
2. This is an evenly spaced set by multiples of 3, the median and mean for an evenly spaced set are equal. Suff
Answer: B

As a side note, can we also assume that there are an odd number of elements because the mean = median is an integer?
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Re: medians [#permalink] New post 07 May 2013, 05:56
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rochak22 wrote:
8. What is the median value of the set R, if for every term in the set, Rn = Rn–1 + 3?
(1) The first term of set R is 15. (2) The mean of set R is 36.


There are certain issues with the question. A set does not have elements in a sequence so there is no question of having Rn and R(n-1)
It needs to be something like this: Elements of a set are arranged in increasing order and it is observed that except for the first element, every element is 3 more than the previous element.

Anyway, I assume that the intent of the question is this.

In that case, notice that this is an arithmetic progression (numbers are evenly spaced).

In an AP, mean = median (since both are the middle term). Hence statement 2 alone is sufficient.
In statement 1, you need to know the total number of elements too to find the median.
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Re: medians [#permalink] New post 07 May 2013, 06:02
VeritasPrepKarishma wrote:
rochak22 wrote:
8. What is the median value of the set R, if for every term in the set, Rn = Rn–1 + 3?
(1) The first term of set R is 15. (2) The mean of set R is 36.


There are certain issues with the question. A set does not have elements in a sequence so there is no question of having Rn and R(n-1)
It needs to be something like this: Elements of a set are arranged in increasing order and it is observed that except for the first element, every element is 3 more than the previous element.

Anyway, I assume that the intent of the question is this.

In that case, notice that this is an arithmetic progression (numbers are evenly spaced).

In an AP, mean = median (since both are the middle term). Hence statement 2 alone is sufficient.
In statement 1, you need to know the total number of elements too to find the median.


VeritasPerepKarishma, is this just the definition of a set that you are referring to, can you provide a resource to look this up? I was under the impression that a set can contain a sequence.
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Re: medians [#permalink] New post 07 May 2013, 06:09
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penguinman wrote:

VeritasPerepKarishma, is this just the definition of a set that you are referring to, can you provide a resource to look this up? I was under the impression that a set can contain a sequence.


A set is a collection of objects, not a sequence.

Check here: http://en.wikipedia.org/wiki/Set_(mathematics)
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Re: medians [#permalink] New post 07 May 2013, 06:13
VeritasPrepKarishma wrote:
penguinman wrote:

VeritasPerepKarishma, is this just the definition of a set that you are referring to, can you provide a resource to look this up? I was under the impression that a set can contain a sequence.


A set is a collection of objects, not a sequence.

Check here: http://en.wikipedia.org/wiki/Set_(mathematics)


Ok, but from http://en.wikipedia.org/wiki/Sequence, a sequence is an ordered list of objects. So why couldn't a set contain a sequence? Isn't the OQ just saying that a set contains a sequence abiding by the equation provided above? I guess I am arguing technicalities but I just want to be clear.

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Re: medians [#permalink] New post 07 May 2013, 07:03
VeritasPrepKarishma wrote:
rochak22 wrote:
8. What is the median value of the set R, if for every term in the set, Rn = Rn–1 + 3?
(1) The first term of set R is 15. (2) The mean of set R is 36.


There are certain issues with the question. A set does not have elements in a sequence so there is no question of having Rn and R(n-1)
It needs to be something like this: Elements of a set are arranged in increasing order and it is observed that except for the first element, every element is 3 more than the previous element.

Anyway, I assume that the intent of the question is this.

In that case, notice that this is an arithmetic progression (numbers are evenly spaced).

In an AP, mean = median (since both are the middle term). Hence statement 2 alone is sufficient.
In statement 1, you need to know the total number of elements too to find the median.


Nice explanations...........Thanks !!.......... karishma ,,,,,,,, but do u think that this is a 700 level question ...........
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Last edited by manishuol on 07 May 2013, 08:59, edited 1 time in total.
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Re: medians [#permalink] New post 07 May 2013, 08:47
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penguinman wrote:

Ok, but from http://en.wikipedia.org/wiki/Sequence, a sequence is an ordered list of objects. So why couldn't a set contain a sequence? Isn't the OQ just saying that a set contains a sequence abiding by the equation provided above? I guess I am arguing technicalities but I just want to be clear.

Thanks!


The question does not talk about sequences. It talks about sets. When one says 'set', you think of a group of numbers, not numbers in a particular sequence. It is confusing to someone who is reading it for the first time. You wonder about Rn and R(n-1) and what they mean. You have to guess the intent of the question. GMAT questions do not do that.
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Re: medians [#permalink] New post 07 May 2013, 09:11
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Nice explanations..................... karishma ,,,,,,,, but do u think that this is a 700 level question ...........

Quote:
No. 600-650



Thanks!! a lot for your reply Karishma ........................ :)
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Re: medians [#permalink] New post 07 May 2013, 11:40
8. What is the median value of the set R, if for every term in the set, Rn = Rn–1 + 3?
(1) The first term of set R is 15. (2) The mean of set R is 36.

For an AP, mean= median. Hence B is sufficient.
A doesn't give any idea about the number of terms and hence we cant find median.
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Re: What is the median value of the set R, if for every term in [#permalink] New post 08 May 2013, 15:22
Quote:
There are certain issues with the question. A set does not have elements in a sequence so there is no question of having Rn and R(n-1)
It needs to be something like this: Elements of a set are arranged in increasing order and it is observed that except for the first element, every element is 3 more than the previous element.


Great insight, VeritasPrepKarishma

It´s similar logic on how: all squares are parallelograms, but not all parallelograms are squares. Accordingly, all sequences are sets, but not all sets are sequences (excluding sequences with no end, infinity, of course)
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Re: What is the median value of the set R, if for every term in [#permalink] New post 09 May 2013, 08:25
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mejia401 wrote:
Quote:
There are certain issues with the question. A set does not have elements in a sequence so there is no question of having Rn and R(n-1)
It needs to be something like this: Elements of a set are arranged in increasing order and it is observed that except for the first element, every element is 3 more than the previous element.


Great insight, VeritasPrepKarishma

It´s similar logic on how: all squares are parallelograms, but not all parallelograms are squares. Accordingly, all sequences are sets, but not all sets are sequences (excluding sequences with no end, infinity, of course)


Actually a 'set' is a collection of objects with no order. A 'sequence' is an ordered list of objects. They are two different things. The only reason I framed the question that way was to keep the original framing involving sets.
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What is the median value of the set R, if for every term in [#permalink] New post 08 Jul 2013, 05:48
B it is .

i would like to add some more to it.
if the AP is consecutive odd even odd evn,which is the case here....then the median=mean in the above case.

Suppose the AP above was r(n)=r(n-1) +4 then ans would not be B. We would require some more information

I hope you get what i am saying.
What is the median value of the set R, if for every term in   [#permalink] 08 Jul 2013, 05:48
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