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

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Math Expert
Joined: 02 Sep 2009
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The average of 5 different numbers is 14. What is the average (arithme  [#permalink]

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22 Aug 2018, 01:27
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35% (medium)

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66% (01:11) correct 34% (01:09) wrong based on 29 sessions

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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]

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22 Aug 2018, 01:35
Given (a+b+c+d+e)/5 = 14
Then a+b+c+d+e =70

From statement 1: Average of two smallest = 5.
Then (a+b)/2 = 5.
a+b = 10. Then c+d+e = 60.
Average of the three largest = 60/3 = 20.
1 is sufficient.

From statement 2: (a+b)/2 = 1/4(c+d+e)/3.
Then a+b = (c+d+e)/6
From question we can say that c+d+e = 70-a-b.
Using this we get 7(a+b) = 70.
a+b = 10.
Then average of c+d+e = 20.
2 is also sufficient.

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Re: The average of 5 different numbers is 14. What is the average (arithme  [#permalink]

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22 Aug 2018, 01:42
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.

St1:- The average (arithmetic mean) of the two smallest numbers is 5.
There are 5 numbers, if 2 numbers are the smallest among them, then the remaining 3 njumbers would be the largest ones.
We know, the sum of 5 numbers & the sum of 2 smallest numbers, hence the sum of remaining 3 Numbers can be calculated.
Therefore average can can be calculated.Actual calculation is not required.
Sufficient.

St2:- The average (arithmetic mean) of the two smallest numbers is 1/4 of the average of the 3 largest numbers.
Here again, the relationship between the largest 3 numbers and the smallest 3 numbers is given.
We can substitute the sum of the smallest numbers vide the given relationship in the total sum and find out the required average.
Sufficient.

Ans. (D)
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The average of 5 different numbers is 14. What is the average (arithme  [#permalink]

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22 Aug 2018, 01:57
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

what we need $$\frac{(c+d+e)}{3}$$ = ?

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

a+b=10

substituting the value we have c+d+e = 60
$$\frac{(c+d+e)}{3}$$ =20
sufficient.

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

$$\frac{(a+b)}{2}$$=$$\frac{(c+d+e)}{12}$$
substituting the value
$$\frac{(c+d+e)}{6}$$ + c+d+e= 70
7(c+d+e)=6*70
$$\frac{(c+d+e)}{3}$$= 20

sufficient

D
The average of 5 different numbers is 14. What is the average (arithme &nbs [#permalink] 22 Aug 2018, 01:57
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