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# M12-30

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Math Expert
Joined: 02 Sep 2009
Posts: 43296

Kudos [?]: 139200 [0], given: 12779

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15 Sep 2014, 23:47
Expert's post
9
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BOOKMARKED
00:00

Difficulty:

75% (hard)

Question Stats:

46% (01:13) correct 54% (00:57) wrong based on 119 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
[Reveal] Spoiler: OA

_________________

Kudos [?]: 139200 [0], given: 12779

Math Expert
Joined: 02 Sep 2009
Posts: 43296

Kudos [?]: 139200 [2], given: 12779

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15 Sep 2014, 23:47
2
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Expert's post
2
This post was
BOOKMARKED
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.

_________________

Kudos [?]: 139200 [2], given: 12779

Manager
Joined: 02 Sep 2014
Posts: 89

Kudos [?]: 261 [1], given: 32

Location: United States
Schools: Haas EWMBA '20
GMAT 1: 770 Q50 V44
GPA: 3.97

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24 Jun 2015, 20:17
1
KUDOS
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.

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

Kudos [?]: 261 [1], given: 32

Math Expert
Joined: 02 Sep 2009
Posts: 43296

Kudos [?]: 139200 [0], given: 12779

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25 Jun 2015, 01:42
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.

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

Edited the typo. Thank you.
_________________

Kudos [?]: 139200 [0], given: 12779

Intern
Status: Senior Consultant
Joined: 12 Mar 2013
Posts: 2

Kudos [?]: 5 [0], given: 1

Location: Italy
GMAT 1: 690 Q46 V38

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22 Dec 2015, 02:26
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate.

Kudos [?]: 5 [0], given: 1

Math Expert
Joined: 02 Sep 2009
Posts: 43296

Kudos [?]: 139200 [0], given: 12779

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22 Dec 2015, 02:29
cappellaiomatto wrote:
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate.

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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Kudos [?]: 139200 [0], given: 12779

Intern
Joined: 30 Apr 2015
Posts: 1

Kudos [?]: [0], given: 0

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28 Jun 2016, 15:05
For the same reason we are considering sentence I true, shouldnt 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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Math Expert
Joined: 02 Sep 2009
Posts: 43296

Kudos [?]: 139200 [0], given: 12779

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30 Jun 2016, 07:21
edutorrescasana wrote:
For the same reason we are considering sentence I true, shouldnt 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

Hope it helps.
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Kudos [?]: 139200 [0], given: 12779

Intern
Joined: 27 Jul 2016
Posts: 16

Kudos [?]: 4 [0], given: 4

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07 Sep 2016, 07:58
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.

Kudos [?]: 4 [0], given: 4

Intern
Joined: 24 Feb 2016
Posts: 2

Kudos [?]: [0], given: 0

GMAT 1: 650 Q47 V33
GMAT 2: 690 Q49 V34

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14 Dec 2016, 06:25
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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Intern
Joined: 05 Feb 2017
Posts: 3

Kudos [?]: 0 [0], given: 2

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05 Dec 2017, 08:52
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.

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...

Last edited by cdl1985 on 05 Dec 2017, 08:57, edited 1 time in total.

Kudos [?]: 0 [0], given: 2

Math Expert
Joined: 02 Sep 2009
Posts: 43296

Kudos [?]: 139200 [0], given: 12779

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05 Dec 2017, 08:57
cdl1985 wrote:
@brunell you need to change the official answer in the gmat club test aswell

The correct answer is A both here and in the tests. What should be changed?
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Kudos [?]: 139200 [0], given: 12779

Re: M12-30   [#permalink] 05 Dec 2017, 08:57
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# M12-30

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