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The average of 5 different numbers is 14. What is the average (arithme

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Bunuel
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The average of 5 different numbers is 14. What is the average (arithme [#permalink] New post   30 Oct 2019, 21:33
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The average of 5 different numbers is 14. What is the average (arithmetic mean) of the 3 largest numbers?


(1) The average (arithmetic mean) of the two smallest numbers is 5.

(2) The average (arithmetic mean) of the two smallest numbers is 1/4 of the average of the 3 largest numbers.
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Re: The average of 5 different numbers is 14. What is the average (arithme [#permalink] New post   31 Oct 2019, 00:33
Bunuel wrote:
The average of 5 different numbers is 14. What is the average (arithmetic mean) of the 3 largest numbers?


(1) The average (arithmetic mean) of the two smallest numbers is 5.

(2) The average (arithmetic mean) of the two smallest numbers is 1/4 of the average of the 3 largest numbers.


given
a+b+c+d+e=70
find c+d+e/3
#1 The average (arithmetic mean) of the two smallest numbers is 5
10+c+d+e=70
c+d+e = 60
avg = 20 sufficeint
#2
The average (arithmetic mean) of the two smallest numbers is 1/4 of the average of the 3 largest numbers.[/quote]
a+b/2 = 1/4 * ( c+d+e)/3
6(a+b) = c+d+e
a+b=10
so c+d+e= 60
sufficient
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Re: The average of 5 different numbers is 14. What is the average (arithme [#permalink] New post   01 Aug 2020, 10:29
For statement 2, how did you figure out that a+b=10?
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Re: The average of 5 different numbers is 14. What is the average (arithme [#permalink] New post   01 Aug 2020, 10:38
1- We can find the Sun of first 2 numbers and deduct it with the total sum to find the AM of last 3 numbers
2- We can use the equation AM of first two numbers is 1/4 AM of last three numbers.

Therefore both statements are sufficient.

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Re: The average of 5 different numbers is 14. What is the average (arithme [#permalink] New post   01 Aug 2020, 10:39
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Logo wrote:
For statement 2, how did you figure out that a+b=10?


We cannot figure out a+b=10 from the 2nd statement.

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The average of 5 different numbers is 14. What is the average (arithme [#permalink] New post   01 Aug 2020, 10:39
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Logo wrote:
For statement 2, how did you figure out that a+b=10?

hemantbafna
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for #2

given
(a+b)/2 = 1/4 * ( c+d+e)/3
which we can write as
6*(a+b) = c+d+e--(1)

we know that
a+b+c+d+e =70
so c+d+e = 70-a-b
substitute this in (1)
we get
6a+6b= 70-a-b
or say
7(a+b) = 70
a+b=10
therefore c+d+e = 60
hope this helps
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Re: The average of 5 different numbers is 14. What is the average (arithme [#permalink] New post   01 Aug 2020, 23:29
hemantbafna wrote:
1- We can find the Sun of first 2 numbers and deduct it with the total sum to find the AM of last 3 numbers
2- We can use the equation AM of first two numbers is 1/4 AM of last three numbers.

Therefore both statements are sufficient.

D

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Can you tell me the equation for second statement?
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Re: The average of 5 different numbers is 14. What is the average (arithme [#permalink]
01 Aug 2020, 23:29
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Bunuel
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