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# If a<b<c<d<e< 110 and the average (arithmetic mean) of a, b,

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If a<b<c<d<e< 110 and the average (arithmetic mean) of a, b, [#permalink]  17 Feb 2017, 06:34
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Question Stats:

78% (00:49) correct 21% (01:38) wrong based on 38 sessions

If a ≤ b ≤ c ≤ d ≤ e ≤ 110 and the average (arithmetic mean) of a, b, c, d, and e is 100, what is the least possible value of a?

A) 0

B) 20

C) 40

D) 60

E) 80
[Reveal] Spoiler: OA

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WE: Business Development (Energy and Utilities)
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Re: If a<b<c<d<e< 110 and the average (arithmetic mean) of a, b, [#permalink]  27 Feb 2017, 05:29
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Expert's post
Explanation

Now we have average of a, b, c, d, e is 100.

$$\frac{a+b+c+d+e}{5}= 100$$ or $$a+b+c+d+e= 500$$.

for a to be least b, c, d and e must be maximum. Now b, c, d and e can take a maximum values 110 each as $$b \leq c \leq d \leq e$$.

$$a + 110 + 110 + 110 + 110 = 500$$

$$a = 60.$$

Hence option D is correct.
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Re: If a<b<c<d<e< 110 and the average (arithmetic mean) of a, b, [#permalink]  28 Mar 2019, 14:35
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Carcass wrote:

If a ≤ b ≤ c ≤ d ≤ e ≤ 110 and the average (arithmetic mean) of a, b, c, d, and e is 100, what is the least possible value of a?

A) 0

B) 20

C) 40

D) 60

E) 80

The average (arithmetic mean) of a, b, c, d, and e is 100
So, (a + b + c + d + e)/5 = 100
This means a + b + c + d + e = 500

What is the least possible value of a?
We already know that a + b + c + d + e = 500
So, to MINIMIZE the value of a, we must MAXIMIZE the values of b, c, d, and e

Since a ≤ b ≤ c ≤ d ≤ e ≤ 110, the MAXIMUM value of b, c, d, and e is 110

Take: a + b + c + d + e = 500
Replace b, c, d and e with 110 to get: a + 110 + 110 + 110 + 110 = 500
Simplify: a + 440 = 500
Solve: a = 60

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com

Re: If a<b<c<d<e< 110 and the average (arithmetic mean) of a, b,   [#permalink] 28 Mar 2019, 14:35
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