The mean of four integers will not change if all the integer : GMAT Problem Solving (PS)
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# The mean of four integers will not change if all the integer

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The mean of four integers will not change if all the integer [#permalink]

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11 Sep 2008, 21:10
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The mean of four integers will not change if all the integers are multiplied by any constant. What is always true about this set of numbers?

I. The mean of the set is 0
II. The sum of the largest member and the smallest member of the set is 0
III. The set contains both positive and negative integers

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III
[Reveal] Spoiler: OA
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11 Sep 2008, 22:08
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arjtryarjtry wrote:
The mean of four integers will not change if all the integers are multiplied by any constant. What is always true about this set of numbers?

I. The mean of the set is 0
II. The sum of the largest member and the smallest member of the set is 0
III. The set contains both positive and negative integers

I only
II only
III only
I and II only
I, II, and III

I. The mean of the set is 0. true.

II. The sum of the largest member and the smallest member of the set is 0.

set 1: -2, -1, 1, 2. true
set 2: -3, -2, -1, 6. false.

III. The set contains both positive and negative integers.

set 1: -2, -1, 1, 2. true
set 2: -3, -2, -1, 6. true

So D. I and III.
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11 Sep 2008, 22:35
IMO I only. the 4 integers could be 0,0,0,0 Hence III ruled out!
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12 Sep 2008, 08:51
ankush83gupta wrote:
IMO I only. the 4 integers could be 0,0,0,0 Hence III ruled out!

are they four integers?

however the question doesnot say four different integers!
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14 Sep 2008, 22:00
[quote="GMAT TIGER]

I. The mean of the set is 0. true.

II. The sum of the largest member and the smallest member of the set is 0.

set 1: -2, -1, 1, 2. true
set 2: -3, -2, -1, 6. false.

III. The set contains both positive and negative integers.

set 1: -2, -1, 1, 2. true
set 2: -3, -2, -1, 6. true

So D. I and III.
[/quote]

I do see a problem here.
What if set 3 = -1, -1, 0, 5?

IMO A.
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Re: The mean of four integers will not change if all the [#permalink]

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03 Feb 2013, 14:27
I have a doubt in this question
If we consider a set {1,2,3,4}, when multiplied with a constant we take that constant as 1 and multiply resulting set will contain the same numbers as the original. so how can the answer be I only.....
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Re: The mean of four integers will not change if all the [#permalink]

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03 Feb 2013, 21:28
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Archit143 wrote:
I have a doubt in this question
If we consider a set {1,2,3,4}, when multiplied with a constant we take that constant as 1 and multiply resulting set will contain the same numbers as the original. so how can the answer be I only.....

The question tells you that 'The mean of four integers will not change if all the integers are multiplied by any constant.'

This means that when you multiply all the four integers by any constant e.g. 1 or 2 or 5 or 100 or -20 etc, you will always get the same mean.
In case of (1, 2, 3, 4}, the mean stays the same only when you multiple each number by 1. When you multiply each number by some other number e.g. 2, the mean changes. So {1, 2, 3, 4} doesn't satisfy our condition.

If the mean is 0, all the numbers will add up to 0.
a+b+c+d = 0
When you multiply this sum by any constant, the sum will remain 0 and hence the new mean will remain 0.
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Re: The mean of four integers will not change if all the integer [#permalink]

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23 Feb 2014, 02:40
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Re: The mean of four integers will not change if all the integer [#permalink]

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01 Mar 2014, 04:25
The possible sets are-
{0,0,0,0,0} and {... -2,-1,0,1,2...}

The question asks "What is always true about this set of numbers". Statement 2 seems to fit the criteria as well. Can someone please explain why statement 2 is not being considered just because there can be sets that satisfy S2 but not the required set {0,0,0,0,0} and {... -2,-1,0,1,2...}?

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Re: The mean of four integers will not change if all the integer [#permalink]

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01 Mar 2014, 06:11
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anindame wrote:
The possible sets are-
{0,0,0,0,0} and {... -2,-1,0,1,2...}

The question asks "What is always true about this set of numbers". Statement 2 seems to fit the criteria as well. Can someone please explain why statement 2 is not being considered just because there can be sets that satisfy S2 but not the required set {0,0,0,0,0} and {... -2,-1,0,1,2...}?

How is {..., -2, -1, 0, 1, 2, ...} a possible set? We are told that the set consists of 4 integers and if all the integers are multiplied by ANY constant, the mean won't change. Does your set satisfy this?
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Re: The mean of four integers will not change if all the integer [#permalink]

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01 Mar 2014, 07:35
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anindame wrote:
The possible sets are-
{0,0,0,0,0} and {... -2,-1,0,1,2...}

The question asks "What is always true about this set of numbers". Statement 2 seems to fit the criteria as well. Can someone please explain why statement 2 is not being considered just because there can be sets that satisfy S2 but not the required set {0,0,0,0,0} and {... -2,-1,0,1,2...}?

consider this, {-3, 0, 1, 2}. The sum of the largest and the smallest is not 0 (-3 + 2 = 1).

However, the mean of the set is still 0, and multiplying any constant to the set will not change the mean of the set.

If you doubt that, consider -3=x, 1=y, 2=z.
x = y + z
Multiplying ANY constant C to the numbers, the sum of the positives and the negatives will not change.
xC = yC + zC = C(y + z)

Hope this helps that II is not ALWAYS true.

Last edited by pocoyama on 01 Mar 2014, 07:53, edited 2 times in total.
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Re: The mean of four integers will not change if all the integer [#permalink]

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01 Mar 2014, 07:44
Bunuel wrote:
anindame wrote:
The possible sets are-
{0,0,0,0,0} and {... -2,-1,0,1,2...}

The question asks "What is always true about this set of numbers". Statement 2 seems to fit the criteria as well. Can someone please explain why statement 2 is not being considered just because there can be sets that satisfy S2 but not the required set {0,0,0,0,0} and {... -2,-1,0,1,2...}?

How is {..., -2, -1, 0, 1, 2, ...} a possible set? We are told that the set consists of 4 integers and if all the integers are multiplied by ANY constant, the mean won't change. Does your set satisfy this?

Sorry.. my bad.. missed the "4 integers" part
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Last edited by anindame on 01 Mar 2014, 07:54, edited 1 time in total.
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Re: The mean of four integers will not change if all the integer [#permalink]

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01 Mar 2014, 07:52
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consider this, {-3, 0, 1, 2}. The sum of the largest and the smallest is not 0 (-3 + 2 = 1).

However, the mean of the set is still 0, and multiplying any constant to the set will not change the mean of the set.

If you doubt that, consider -3=x, 1=y, 2=z.
x = y + z
Multiplying ANY constant C to the numbers, the sum of the positives and the negatives will not change.
xC = yC + zC = C(y + z)

Hope this helps that II is not ALWAYS true.

Right!! Thanks
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Re: The mean of four integers will not change if all the integer [#permalink]

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06 Sep 2015, 19:03
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Re: The mean of four integers will not change if all the integer [#permalink]

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07 Nov 2015, 21:51
i tested with sets

{-2 -1 1 2}
{0 0 0 0}
{-3 -2 -1 6}

able to eliminate all but A, in each case the mean is 0
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Re: The mean of four integers will not change if all the integer [#permalink]

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04 Dec 2016, 05:31
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Re: The mean of four integers will not change if all the integer   [#permalink] 04 Dec 2016, 05:31
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