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

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

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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: always true  [#permalink]

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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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Re: always true  [#permalink]

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IMO I only. the 4 integers could be 0,0,0,0 Hence III ruled out!
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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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[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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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 integer  [#permalink]

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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...}?

The question asks "What is always true about this set of numbers". Statement 2 is always true about this set of numbers. Or is there some other possible set for the answer that S2 does not satisfy?
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Re: The mean of four integers will not change if all the integer  [#permalink]

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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...}?

The question asks "What is always true about this set of numbers". Statement 2 is always true about this set of numbers. Or is there some other possible set for the answer that S2 does not satisfy?

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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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...}?

The question asks "What is always true about this set of numbers". Statement 2 is always true about this set of numbers. Or is there some other possible set for the answer that S2 does not satisfy?

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.

Originally posted by pocoyama on 01 Mar 2014, 08:35.
Last edited by pocoyama on 01 Mar 2014, 08:53, 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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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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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: The mean of four integers will not change if all the integer  [#permalink]

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1
Hi All,

In Roman Numeral questions, it's often easiest to DISPROVE the Roman Numerals, if possible (so that you can eliminate answer choices).

Here, we're told that the MEAN of 4 integers will NOT change if each integer is multiplied by the same (re: ANY) constant. We're asked which of the Roman Numerals is ALWAYS TRUE. We can TEST VALUES to eliminate options....

II. The sum of the largest and smallest is 0

IF...the set is {-3, 0, 1, 2} then the mean would stay the same, but the sum of the largest and smallest is NOT 0.
Roman Numeral II is NOT true.
Eliminate Answers B, D and E

III. The set contains BOTH positive AND negative numbers

IF....the set is {0, 0, 0, 0} then the mean would stay the same and the set does NOT contain both positive and negative numbers.
Roman Numeral III is NOT true.

There's only one answer left....

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

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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

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III

Here's what I used, mostly because I suck at plugging in values

4 integers w,x,y,z
Average = (w+x+y+z)/4

The Mean does not change when multiplied by any constant so,
(w+x+y+z)/4 = a(w+x+y+z)/4 ; a is the constant here
=> (w+x+y+z)(1-a)=0
And so we get that either the constant a is 1 or (w+x+y+z) = 0;

I is true because w+x+y+z=0 and therefore the mean is 0
II there is no reason for this to be true
III Not always true since {0,0,0,0} satisfies the parameters of the question
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Re: The mean of four integers will not change if all the integer  [#permalink]

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Mean of ‘n’ no of integers gets multiplied by ‘a’ when all the numbers are multiplied by ‘a’.
So if ‘y’ is the mean of 4 numbers p,q,r and s, then 4y is the mean of 4p,4q,4r and 4s.
1. The above given statement is true only if the mean of four numbers is 0. Then if the numbers are multiplied with any constant the mean will still be 0.Hence, necessarily true.
2. Let’s say 4 numbers be -6, -2 , 0 ,8. Here the mean is 0 but the sum of largest and smallest number is not 0. Hence, not necessarily true.
3. The set could be 0,0,0,0. Hence, not necessarily true. Re: The mean of four integers will not change if all the integer   [#permalink] 18 Dec 2018, 23:42
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