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M12-30

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M12-30  [#permalink]

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New post 16 Sep 2014, 00:47
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  75% (hard)

Question Stats:

47% (01:08) correct 53% (00:56) wrong based on 130 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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Re M12-30  [#permalink]

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New post 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.


Answer: A
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Re: M12-30  [#permalink]

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New post 24 Jun 2015, 21:17
1
Bunuel wrote:
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 \(\{-3, 1, 2\}\).

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


Answer: A


In the explanation for II, it needs to have 4 numbers. But doesnt affect final answer.
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New post 25 Jun 2015, 02:42
82vkgmat wrote:
Bunuel wrote:
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 \(\{-3, 1, 2\}\).

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


Answer: A


In the explanation for II, it needs to have 4 numbers. But doesnt affect final answer.


Edited the typo. Thank you.
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Re M12-30  [#permalink]

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New post 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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New post 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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Re M12-30  [#permalink]

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New post 28 Jun 2016, 16:05
For the same reason we are considering sentence I true, shouldn`t sentence II be true as well? 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? Tks
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New post 30 Jun 2016, 08:21
edutorrescasana wrote:
For the same reason we are considering sentence I true, shouldn`t sentence II be true as well? 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? Tks


Please check here: the-mean-of-four-integers-will-not-change-if-all-the-integer-70142.html

Hope it helps.
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Re: M12-30  [#permalink]

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New post 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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Re: M12-30  [#permalink]

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New post 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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M12-30  [#permalink]

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New post Updated on: 05 Dec 2017, 09:57
Bunuel wrote:
82vkgmat wrote:
Bunuel wrote:
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 \(\{-3, 1, 2\}\).

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


Answer: A


In the explanation for II, it needs to have 4 numbers. But doesnt affect final answer.


Edited the typo. Thank you.



@brunell you need to change the official answer in the gmat club test aswell


Forget my comment...

Originally posted by cdl1985 on 05 Dec 2017, 09:52.
Last edited by cdl1985 on 05 Dec 2017, 09:57, edited 1 time in total.
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New post 05 Dec 2017, 09:57
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New post 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?
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New post 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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: M12-30 &nbs [#permalink] 24 Mar 2018, 09:06
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