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The average (arithmetic mean) of 3 different positive integers is 100

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The average (arithmetic mean) of 3 different positive integers is 100  [#permalink]

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New post 20 Nov 2018, 08:19
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Question Stats:

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The average (arithmetic mean) of 3 different positive integers is 100 and the largest of these 3 integers is 120. What is the least possible value of the smallest of these 3 integers?

(A) 1
(B) 10
(C) 61
(D) 71
(E) 80

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Re: The average (arithmetic mean) of 3 different positive integers is 100  [#permalink]

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New post 20 Nov 2018, 10:24
\(\frac{(2x+120)}{3} =100\)

\(2x+120=300\)

\(2x=180\)

\(x =90\)

so 120 +90+90 to minimize one value maximize secnd one 120+119+61

IMO: C :)
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Re: The average (arithmetic mean) of 3 different positive integers is 100  [#permalink]

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New post 20 Nov 2018, 13:32
(a+b+c)/3 = 100
a+b+120 = 300
=> a+b = 180 =>a = 180 - b
b<120 => a>60
smallest a is 61 => C
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Re: The average (arithmetic mean) of 3 different positive integers is 100  [#permalink]

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New post 20 Nov 2018, 14:25
HKD1710 wrote:
The average (arithmetic mean) of 3 different positive integers is 100 and the largest of these 3 integers is 120. What is the least possible value of the smallest of these 3 integers?

(A) 1
(B) 10
(C) 61
(D) 71
(E) 80

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second largest integer is 120-1=119
so least value of smallest must be (300-120)-119=61
C
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Re: The average (arithmetic mean) of 3 different positive integers is 100  [#permalink]

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New post 20 Nov 2018, 15:26
Average=100={120+x+y}/3
X+y=180
Assume x to be smallest and start plugging in the answers to get y.
Now neither x nor y can be larger than 120. So a and b makes y greater than 120. Therefore are incorrect. From the rest 61 is the smallest.

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Re: The average (arithmetic mean) of 3 different positive integers is 100  [#permalink]

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New post 27 Nov 2018, 12:43
Avg of 3 nos will be -
(x+ 2nd largest + largest)/3
=> (x+ 119 +120) / 3 =100
=> x= 61 (C)
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Re: The average (arithmetic mean) of 3 different positive integers is 100 &nbs [#permalink] 27 Nov 2018, 12:43
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The average (arithmetic mean) of 3 different positive integers is 100

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