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Set M consists of 20 evenly spaced integers, 10 numbers of w

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Set M consists of 20 evenly spaced integers, 10 numbers of w [#permalink] New post 30 Aug 2018, 07:38
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31% (00:28) correct 68% (00:34) wrong based on 38 sessions
Set M consists of 20 evenly spaced integers, 10 numbers of which are positive and 10 of which are negative.

Quantity A
Quantity B
The average (arithmetic mean) of all the numbers in set M
\(0\)


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: Set M consists of 20 evenly spaced integers, 10 numbers of w [#permalink] New post 30 Aug 2018, 10:04
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Expert's post
sandy wrote:
Set M consists of 20 evenly spaced integers, 10 numbers of which are positive and 10 of which are negative.

Quantity A
Quantity B
The average (arithmetic mean) of all the numbers in set M
\(0\)


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.


Nice question!

ASIDE: I've never been a fan of the term "EVENLY spaced". I worry that students believe that the difference between consecutive values must be EVEN. SO, I typically write "EQUALLY spaced."

Okay, let's solve this question by coming up with some 20-number sets that satisfy the given conditions.

CASE A: The numbers are {-19, -17, -15, -13, -11, -9, -7, -5, -3, -1, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19}
Here, the mean of the set is 0
So, in this case, the two quantities are EQUAL

CASE B: The numbers are {-28, -25, -22, -19, -16, -13, -10, -7, -4, -1, 2, 5, 8, 11, 14, 17, 20, 23, 26, 29}
Here, the mean of the set is NOT zero
So, in this case, the two quantities are NOT EQUAL

Answer: D

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Re: Set M consists of 20 evenly spaced integers, 10 numbers of w [#permalink] New post 14 Jan 2019, 01:38
Expert's post
GreenlightTestPrep wrote:
sandy wrote:
Set M consists of 20 evenly spaced integers, 10 numbers of which are positive and 10 of which are negative.

Quantity A
Quantity B
The average (arithmetic mean) of all the numbers in set M
\(0\)


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.


Nice question!

ASIDE: I've never been a fan of the term "EVENLY spaced". I worry that students believe that the difference between consecutive values must be EVEN. SO, I typically write "EQUALLY spaced."

Okay, let's solve this question by coming up with some 20-number sets that satisfy the given conditions.

CASE A: The numbers are {-19, -17, -15, -13, -11, -9, -7, -5, -3, -1, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19}
Here, the mean of the set is 0
So, in this case, the two quantities are EQUAL

CASE B: The numbers are {-28, -25, -22, -19, -16, -13, -10, -7, -4, -1, 2, 5, 8, 11, 14, 17, 20, 23, 26, 29}
Here, the mean of the set is NOT zero
So, in this case, the two quantities are NOT EQUAL

Answer: D

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Wow, great stuff.
Re: Set M consists of 20 evenly spaced integers, 10 numbers of w   [#permalink] 14 Jan 2019, 01:38
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Set M consists of 20 evenly spaced integers, 10 numbers of w

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