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The mean of four integers will not change if all the integer [#permalink]
 11 Sep 2008, 22:10
Question Stats:
34% (01:50) correct
65% (00:38) wrong based on 6 sessions
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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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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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]
03 Feb 2013, 15:27
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]
03 Feb 2013, 22:28
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
[#permalink]
03 Feb 2013, 22:28
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