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# Is the average (arithmetic mean) of 5 different positive

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Is the average (arithmetic mean) of 5 different positive [#permalink]

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07 May 2012, 08:55
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Is the average (arithmetic mean) of 5 different positive integers at least 30?

(1) Each of the integers is a multiple of 10
(2) The sum of the 5 integers is 160
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Re: Is the average (arithmetic mean) of 5 different positive [#permalink]

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07 May 2012, 09:05
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Is the average (arithmetic mean) of 5 different positive integers at least 30?

It's almost always better to express the average in terms of the sum. The question basically asks whether the sum of 5 different positive integers is at least 5*30=150.

(1) Each of the integers is a multiple of 10 --> the least values of these 5 different positive integers are: 10, 20, 30, 40, and 50 --> the sum = 150. Sufficient.

(2) The sum of the 5 integers is 160. Directly answers the question. Sufficient.

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Re: Is the average (arithmetic mean) of 5 different positive [#permalink]

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15 Sep 2012, 07:25
Bunuel wrote:
Is the average (arithmetic mean) of 5 different positive integers at least 30?

It's almost always better to express the average in terms of the sum. The question basically asks whether the sum of 5 different positive integers is at least 5*30=150.

(1) Each of the integers is a multiple of 10 --> the least values of these 5 different positive integers are: 10, 20, 30, 40, and 50 --> the sum = 150. Sufficient.

(2) The sum of the 5 integers is 160. Directly answers the question. Sufficient.

Bunuel... nice way to explain.

However, don't you think statement A and B contradicts each other.

For example, As per statement 1, 5 numbers are multiple of 10; hence average should be mid number. (In your list 30 is the average)

As per statement 2, The average is 160/5 = 32. Now 32 is not the multiple of 10. By no means we can get 32 as average and 5 numbers multiple of 10

Please explain, am I missing something as this is GMAT prep problem
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Re: Is the average (arithmetic mean) of 5 different positive [#permalink]

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15 Sep 2012, 08:14
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nishtil wrote:
Bunuel wrote:
Is the average (arithmetic mean) of 5 different positive integers at least 30?

It's almost always better to express the average in terms of the sum. The question basically asks whether the sum of 5 different positive integers is at least 5*30=150.

(1) Each of the integers is a multiple of 10 --> the least values of these 5 different positive integers are: 10, 20, 30, 40, and 50 --> the sum = 150. Sufficient.

(2) The sum of the 5 integers is 160. Directly answers the question. Sufficient.

Bunuel... nice way to explain.

However, don't you think statement A and B contradicts each other.

For example, As per statement 1, 5 numbers are multiple of 10; hence average should be mid number. (In your list 30 is the average)

As per statement 2, The average is 160/5 = 32. Now 32 is not the multiple of 10. By no means we can get 32 as average and 5 numbers multiple of 10

Please explain, am I missing something as this is GMAT prep problem

We are not told that the integers are evenly spaced so it's not necessary that the average is the middle number (in my example, yes, I consider evenly spaced set, but it's just one of the cases). For example the set could be 10, 20, 30, 40, and 60 --> sum=160 --> average=160/5=32.

Hope it's clear.
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Re: Is the average (arithmetic mean) of 5 different positive [#permalink]

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25 Dec 2012, 14:36
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Bunuel wrote:
Is the average (arithmetic mean) of 5 different positive integers at least 30?

It's almost always better to express the average in terms of the sum. The question basically asks whether the sum of 5 different positive integers is at least 5*30=150.

(1) Each of the integers is a multiple of 10 --> the least values of these 5 different positive integers are: 10, 20, 30, 40, and 50 --> the sum = 150. Sufficient.

(2) The sum of the 5 integers is 160. Directly answers the question. Sufficient.

why cannot we consider 0,10,20,30,40? Isn't 0 taken as both positive and negative?

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Re: Is the average (arithmetic mean) of 5 different positive [#permalink]

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26 Dec 2012, 03:38
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Amateur wrote:
Bunuel wrote:
Is the average (arithmetic mean) of 5 different positive integers at least 30?

It's almost always better to express the average in terms of the sum. The question basically asks whether the sum of 5 different positive integers is at least 5*30=150.

(1) Each of the integers is a multiple of 10 --> the least values of these 5 different positive integers are: 10, 20, 30, 40, and 50 --> the sum = 150. Sufficient.

(2) The sum of the 5 integers is 160. Directly answers the question. Sufficient.

why cannot we consider 0,10,20,30,40? Isn't 0 taken as both positive and negative?

Positive numbers are greater than zero and negative numbers are less than zero. Zero is neither positive nor negative.
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Re: Is the average (arithmetic mean) of 5 different positive [#permalink]

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28 Dec 2012, 18:45
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Yea 0 is neither position nor negative. So the first five different positive numbers are 10,20,30,40,50.

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Re: Is the average (arithmetic mean) of 5 different positive [#permalink]

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20 Jan 2013, 07:04
Bunuel wrote:
Is the average (arithmetic mean) of 5 different positive integers at least 30?

It's almost always better to express the average in terms of the sum. The question basically asks whether the sum of 5 different positive integers is at least 5*30=150.

(1) Each of the integers is a multiple of 10 --> the least values of these 5 different positive integers are: 10, 20, 30, 40, and 50 --> the sum = 150. Sufficient.

(2) The sum of the 5 integers is 160. Directly answers the question. Sufficient.

The way I understood statement 1 is that since each of the integers is a multiple of 10 it could be: 10, 20, 20, 20, 20. How do you know that it must be increasing in order? (probably just a language issue).

Thanks!
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Re: Is the average (arithmetic mean) of 5 different positive [#permalink]

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20 Jan 2013, 10:06
Says "5 different numbers" so you can't have 20 20 20 20. 10 20 30 40 50 is the lowest possible number w/ the given constraints.

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Re: Is the average (arithmetic mean) of 5 different positive [#permalink]

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15 Jun 2013, 07:17
Bunuel wrote:
Is the average (arithmetic mean) of 5 different positive integers at least 30?

It's almost always better to express the average in terms of the sum. The question basically asks whether the sum of 5 different positive integers is at least 5*30=150.

(1) Each of the integers is a multiple of 10 --> the least values of these 5 different positive integers are: 10, 20, 30, 40, and 50 --> the sum = 150. Sufficient.

(2) The sum of the 5 integers is 160. Directly answers the question. Sufficient.

One question: is zero not considered as a multiple of any number?

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Re: Is the average (arithmetic mean) of 5 different positive [#permalink]

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15 Jun 2013, 07:22
BankerRUS wrote:
Bunuel wrote:
Is the average (arithmetic mean) of 5 different positive integers at least 30?

It's almost always better to express the average in terms of the sum. The question basically asks whether the sum of 5 different positive integers is at least 5*30=150.

(1) Each of the integers is a multiple of 10 --> the least values of these 5 different positive integers are: 10, 20, 30, 40, and 50 --> the sum = 150. Sufficient.

(2) The sum of the 5 integers is 160. Directly answers the question. Sufficient.

One question: is zero not considered as a multiple of any number?

Yes, 0 is a multiple of every integer except 0 itself.
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Re: Is the average (arithmetic mean) of 5 different positive [#permalink]

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01 Sep 2015, 20:23
Hi Bunuel,
can we consider 0 as multiple of 10?

Bunuel wrote:
Is the average (arithmetic mean) of 5 different positive integers at least 30?

It's almost always better to express the average in terms of the sum. The question basically asks whether the sum of 5 different positive integers is at least 5*30=150.

(1) Each of the integers is a multiple of 10 --> the least values of these 5 different positive integers are: 10, 20, 30, 40, and 50 --> the sum = 150. Sufficient.

(2) The sum of the 5 integers is 160. Directly answers the question. Sufficient.

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Is the average (arithmetic mean) of 5 different positive [#permalink]

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01 Sep 2015, 20:36
sunita123 wrote:
Hi Bunuel,
can we consider 0 as multiple of 10?

Bunuel wrote:
Is the average (arithmetic mean) of 5 different positive integers at least 30?

It's almost always better to express the average in terms of the sum. The question basically asks whether the sum of 5 different positive integers is at least 5*30=150.

(1) Each of the integers is a multiple of 10 --> the least values of these 5 different positive integers are: 10, 20, 30, 40, and 50 --> the sum = 150. Sufficient.

(2) The sum of the 5 integers is 160. Directly answers the question. Sufficient.

0 is a multiple of all positive integers.

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Re: Is the average (arithmetic mean) of 5 different positive [#permalink]

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01 Sep 2015, 21:04
Right. so why we are not considering , 0,10,20,30 & 40 here?

Engr2012 wrote:
sunita123 wrote:
Hi Bunuel,
can we consider 0 as multiple of 10?

Bunuel wrote:
Is the average (arithmetic mean) of 5 different positive integers at least 30?

It's almost always better to express the average in terms of the sum. The question basically asks whether the sum of 5 different positive integers is at least 5*30=150.

(1) Each of the integers is a multiple of 10 --> the least values of these 5 different positive integers are: 10, 20, 30, 40, and 50 --> the sum = 150. Sufficient.

(2) The sum of the 5 integers is 160. Directly answers the question. Sufficient.

0 is a multiple of all positive integers.

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Re: Is the average (arithmetic mean) of 5 different positive [#permalink]

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01 Sep 2015, 21:11
sunita123 wrote:
Right. so why we are not considering , 0,10,20,30 & 40 here?

Because the set is composed of POSITIVE integers and 0 is neither positive nor negative.

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Re: Is the average (arithmetic mean) of 5 different positive [#permalink]

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29 Dec 2016, 07:46
piyushksharma wrote:
Is the average (arithmetic mean) of 5 different positive integers at least 30?

(1) Each of the integers is a multiple of 10
(2) The sum of the 5 integers is 160

1) AM of least 5 multiple of ten=10+20+30+40+50/3=30 => SUFFICIENT
2) Sum of 5 ints=160 => AM>30 => SUFFICIENT

D.
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Re: Is the average (arithmetic mean) of 5 different positive [#permalink]

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29 Dec 2016, 11:11
piyushksharma wrote:
Is the average (arithmetic mean) of 5 different positive integers at least 30?

(1) Each of the integers is a multiple of 10
(2) The sum of the 5 integers is 160

As per statement 1:

Multiples of 10: 10+20+30+40+50 = 150

150/5 = 30 Sufficient

As per statement 2:

Sum is 160 so 160/5 = 32

Sufficient

(D)
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Re: Is the average (arithmetic mean) of 5 different positive   [#permalink] 29 Dec 2016, 11:11
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