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Joined: 20 Feb 2017
Posts: 2506
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A set of 5 numbers has an average of 50. The largest element in the se
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17 Jul 2021, 23:32
17 Jul 2021, 23:32
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A set of 5 numbers has an average of 50. The largest element in the set is 5 greater than 3 times the smallest element in the set. If the median of the set equals the mean, what is the largest possible value in the set?
(A) 85
(B) 86
(C) 88
(D) 91
(E) 92
(A) 85
(B) 86
(C) 88
(D) 91
(E) 92
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Re: A set of 5 numbers has an average of 50. The largest element in the se
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18 Jul 2021, 00:51
18 Jul 2021, 00:51
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GeminiHeat wrote:
A set of 5 numbers has an average of 50. The largest element in the set is 5 greater than 3 times the smallest element in the set. If the median of the set equals the mean, what is the largest possible value in the set?
(A) 85
(B) 86
(C) 88
(D) 91
(E) 92
(A) 85
(B) 86
(C) 88
(D) 91
(E) 92
Let the numbers be a, b , c , d, and e
\(\frac{a + b + c + d + e}{5} = 50\)
i.e. \(a + b + c + d + e = 250\)
Also, \(c = 50\) and \(e = 3a + 5\)
So, \(a + b + 50 + d + (3a + 5) = 250\)
In order to maximize \(e = (3a + 5)\) - we must maximize \(a\)
This must be done by taking the share of \(d\) and \(b\), and giving it to \(e\)
Therefore, \(d = 50\) and \(b = a\)
\(a + a + 50 + 50 + (3a + 5) = 250\)
\(5a + 105 = 250\)
\(5a = 145\)
\(a = 29\)
i.e. \(e = 3(29) + 5 = 92\)
Hence, option E
Re: A set of 5 numbers has an average of 50. The largest element in the se
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02 Apr 2025, 06:20
02 Apr 2025, 06:20
Hello from the GRE Prep Club BumpBot!
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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
