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The mean of four integers will not change if all the integer [#permalink]
11 Sep 2008, 21:10

2

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Difficulty:

45% (medium)

Question Stats:

33% (01:55) correct
66% (00:56) wrong based on 95 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

Re: The mean of four integers will not change if all the [#permalink]
03 Feb 2013, 21:28

2

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Expert's post

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.
_________________

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

Re: The mean of four integers will not change if all the integer [#permalink]
01 Mar 2014, 06:11

1

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Expert's post

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?
_________________

Re: The mean of four integers will not change if all the integer [#permalink]
01 Mar 2014, 07:35

1

This post received KUDOS

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.

Last edited by cssmarimo on 01 Mar 2014, 07:53, edited 2 times in total.

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

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

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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

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?
_________________

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

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?

Sorry.. my bad.. missed the "4 integers" part
_________________

Re: The mean of four integers will not change if all the integer [#permalink]
01 Mar 2014, 07:52

cssmarimo wrote:

bumpbot wrote:

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

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)