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# For any 3 given numbers, which of the following is always equivalent

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For any 3 given numbers, which of the following is always equivalent  [#permalink]

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27 Jul 2016, 01:48
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For any 3 given numbers, which of the following is always equivalent to adding the 3 numbers together and then dividing the sum by 3?

I. Ordering the 3 numbers numerically, from highest to lowest, and then selecting the middle number.
II. Dividing each of the numbers by 3 and then adding the results together.
III. Multiplying each number by 6, adding the resulting products together, and then dividing the sum by 9.

A. I only
B. II only
C. I and II only
D. II and III only
E. None of the above

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Re: For any 3 given numbers, which of the following is always equivalent  [#permalink]

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27 Jul 2016, 02:08
Let the 3 numbers be x, y and z.

Question: Which of the following is equivalent to (x + y + z)/3

I. Ordering the 3 numbers numerically, from highest to lowest, and then selecting the middle number. --> Not always equivalent Eg: 111 and 141
II. Dividing each of the numbers by 3 and then adding the results together. --> x/3 + y/3 + z/3 = (x + y + z)/3 --> Equivalent
III. Multiplying each number by 6, adding the resulting products together, and then dividing the sum by 9. --> (6x + 6y + 6z)/9 = 2(x + y + z)/3 --> Not equivalent

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Re: For any 3 given numbers, which of the following is always equivalent  [#permalink]

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27 Jul 2016, 03:18
Bunuel wrote:
For any 3 given numbers, which of the following is always equivalent to adding the 3 numbers together and then dividing the sum by 3?

I. Ordering the 3 numbers numerically, from highest to lowest, and then selecting the middle number.
II. Dividing each of the numbers by 3 and then adding the results together.
III. Multiplying each number by 6, adding the resulting products together, and then dividing the sum by 9.

A. I only
B. II only
C. I and II only
D. II and III only
E. None of the above

Let's take the three numbers as a,b and c, as per the stem, it is given that adding three number and dividing the numbers by 3 i.e. a+b+c/3 ---eq 1.

Now we need to check which of the following options are equal
I. Ordering the 3 numbers numerically, from highest to lowest, and then selecting the middle number.

Here we can take a>b>c or b>c>a or c>a>b, then we asked to take the middle number, the number can be b,c or a respectively and this is not equal to eq1.

II. Dividing each of the numbers by 3 and then adding the results together.

a/3, b/3 and c/3 => we get a+b+c/3 ---equal to eq1.

III. Multiplying each number by 6, adding the resulting products together, and then dividing the sum by 9.

6a,6b and 6c then adding and dividing by 9 => 6(a+b+c)/9 => 2(a+b+c)/3 and this is not equal to eq1.

Only option 2 is looks good.

OA please...will correct if I missed anything..
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Re: For any 3 given numbers, which of the following is always equivalent  [#permalink]

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27 Jul 2016, 05:52
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Bunuel wrote:
For any 3 given numbers, which of the following is always equivalent to adding the 3 numbers together and then dividing the sum by 3?

I. Ordering the 3 numbers numerically, from highest to lowest, and then selecting the middle number.
II. Dividing each of the numbers by 3 and then adding the results together.
III. Multiplying each number by 6, adding the resulting products together, and then dividing the sum by 9.

A. I only
B. II only
C. I and II only
D. II and III only
E. None of the above

I was wondering by highest to lowest does it mean that they have to be consecutive numbers? e.g. 6, 5, 4 or 4, 3, 2 ?
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Re: For any 3 given numbers, which of the following is always equivalent  [#permalink]

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27 Jul 2016, 06:15
AtifS wrote:
Bunuel wrote:
For any 3 given numbers, which of the following is always equivalent to adding the 3 numbers together and then dividing the sum by 3?

I. Ordering the 3 numbers numerically, from highest to lowest, and then selecting the middle number.
II. Dividing each of the numbers by 3 and then adding the results together.
III. Multiplying each number by 6, adding the resulting products together, and then dividing the sum by 9.

A. I only
B. II only
C. I and II only
D. II and III only
E. None of the above

I was wondering by highest to lowest does it mean that they have to be consecutive numbers? e.g. 6, 5, 4 or 4, 3, 2 ?

Hi,

It does not mean that it has to be consecutive. It can be anything.
For example: Consider 1, 4 and 1 --> (1 + 4 + 1)/3 = 2 --> Sort the numbers. Middle number is 1 and its not equal to 2
Consider one more example in which all 3 numbers are equal (x, x, x). For this case middle number will always be equal to (x + x + x)/3
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Re: For any 3 given numbers, which of the following is always equivalent  [#permalink]

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27 Jul 2016, 11:03
Bunuel wrote:
For any 3 given numbers, which of the following is always equivalent to adding the 3 numbers together and then dividing the sum by 3?

I. Ordering the 3 numbers numerically, from highest to lowest, and then selecting the middle number.
II. Dividing each of the numbers by 3 and then adding the results together.
III. Multiplying each number by 6, adding the resulting products together, and then dividing the sum by 9.

A. I only
B. II only
C. I and II only
D. II and III only
E. None of the above

I. Ordering the 3 numbers numerically, from highest to lowest, and then selecting the middle number.
This will only be true if the numbers are consecutive integers.

II. Dividing each of the numbers by 3 and then adding the results together.
Correct.
a+b+c/3= a/3+b/3+c/3

III. Multiplying each number by 6, adding the resulting products together, and then dividing the sum by 9.
6a+6b+6c/9= 2a+2b+2c/3 and this is not equal to a+b+c/3

Only option 2 satisfies the condition.
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Re: For any 3 given numbers, which of the following is always equivalent  [#permalink]

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27 Oct 2018, 13:41
I did the mistake of taking consecutive numbers because of which option A was always correct.
Re: For any 3 given numbers, which of the following is always equivalent   [#permalink] 27 Oct 2018, 13:41
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