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# M12-30

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 00:47
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Difficulty:

75% (hard)

Question Stats:

47% (01:38) correct 53% (01:35) wrong based on 96 sessions

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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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16 Sep 2014, 00:47
2
1
Official Solution:

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

If the constant is 0, the mean of the new set is 0. Thus, the mean of the original set has to be 0 as well.

II is not necessarily true. Consider $$\{-3, 0, 1, 2\}$$.

III is not necessarily true. The set can contain only zeros.

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22 Dec 2015, 03:26
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate.
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22 Dec 2015, 03:29
cappellaiomatto wrote:
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate.

Please be a little bit more specific when asking a question.

As for the question check alternative solutions here: the-mean-of-four-integers-will-not-change-if-all-the-integer-70142.html

Hope it helps.
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07 Sep 2016, 08:58
edutorrescasana wrote:
Considering "mean of four integers will not change if all the integers are multiplied by any constant", shouldnt all the numbers be 0 and then the sum of the largest and smallest be 0?

All numbers being zero is a valid set, but not the only valid set. The question asks "What is always true..."

Possible sets of 4 integers whose mean does not change if all a integers are multiple by any constant:
0, 0 ,0 0
-2, -1, -2, 2
-3, 0, 1, 2

The largest and smallest integers in the last example do not equal zero.
There are not positive and negative integers in the first set.
All have a mean of 0.
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Joined: 24 Feb 2016
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14 Dec 2016, 07:25
It is a very interesting question, because we may consider 1 also as the mean of the set, but it is discarded once you realize that the constant that multiplies the mean can be positive or negative. In this case, 0 remains as the only mean.

Statements II and III were easy to discard thereafter.
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24 Mar 2018, 06:01
If the constant multiplied is equal to 1, then option 1 also fails.

I am not sure if I am missing something. A constant can be any real integer right?
Math Expert
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Posts: 55150

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24 Mar 2018, 09:06
Aswath Kumar wrote:
If the constant multiplied is equal to 1, then option 1 also fails.

I am not sure if I am missing something. A constant can be any real integer right?

The mean of four integers will not change if all the integers are multiplied by ANY constant.

Of course the mean won't change if you multiply all the integers by 1 and in this case the mean could be any number but if we want the mean not to change when we multiply by ANY constant than the mean must be 0.

Check for more here: https://gmatclub.com/forum/the-mean-of- ... 70142.html
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08 Sep 2018, 01:58
I think this is a poor-quality question and I don't agree with the explanation. What if the set was {1,1,1,1} and the constant was 1. The above assumption of the set and constant will not have a mean of 0. The question doesn't specify whether the integers are "distinct".
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08 Sep 2018, 02:05
sumitkar007 wrote:
I think this is a poor-quality question and I don't agree with the explanation. What if the set was {1,1,1,1} and the constant was 1. The above assumption of the set and constant will not have a mean of 0. The question doesn't specify whether the integers are "distinct".

Please re-read the question and solution more carefully:

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?
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08 Sep 2018, 02:41
Arrgghh Ok got it now. Thanks Bunuel!
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17 Nov 2018, 08:05
I think this is a high-quality question and I agree with explanation.
Intern
Joined: 04 Feb 2018
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27 Mar 2019, 07:50
I don't agree with the explanation. what if the constant is 1?
The mean of the set will still be the same.
Math Expert
Joined: 02 Sep 2009
Posts: 55150

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27 Mar 2019, 07:52
shankargp wrote:
I don't agree with the explanation. what if the constant is 1?
The mean of the set will still be the same.

I tried answering this doubt in my posts above. Please re-read the discussion. Hope it helps.
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Re: M12-30   [#permalink] 27 Mar 2019, 07:52
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# M12-30

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