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The average (arithmetic mean) of 4 positive integers is 50.

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The average (arithmetic mean) of 4 positive integers is 50.  [#permalink]

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The average (arithmetic mean) of 4 positive integers is 50. If the average of 2 of these integers is 45, what is the greatest possible value that one of the other 2 integers can have?

A. 55
B. 65
C. 100
D. 109
E. 115
Spoiler: OA

Originally posted by iyersu on 21 Dec 2013, 03:31.
Last edited by Bunuel on 21 Dec 2013, 04:05, edited 1 time in total.
Renamed the topic and edited the question.
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Re: The average (arithmetic mean) of 4 positive integers is 50.  [#permalink]

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New post 21 Dec 2013, 04:16
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iyersu wrote:
The average (arithmetic mean) of 4 positive integers is 50. If the average of 2 of these integers is 45, what is the greatest possible value that one of the other 2 integers can have?

A. 55
B. 65
C. 100
D. 109
E. 115


The sum of 4 integers is 4*50 = 200.
The sum of 2 integers is 2*45 = 90.

Thus, the sum of the other 2 integers is 200 - 90 = 110. Since we know that the integers are positive then the greatest one from these two can be 109, the other one being 1.

Answer: D.

Hope it's clear.
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Re: The average (arithmetic mean) of 4 positive integers is 50.  [#permalink]

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New post 10 Sep 2014, 22:01
1
iyersu wrote:
The average (arithmetic mean) of 4 positive integers is 50. If the average of 2 of these integers is 45, what is the greatest possible value that one of the other 2 integers can have?

A. 55
B. 65
C. 100
D. 109
E. 115


a + b + c + d = 200

a + b = 90

c + d = 110

Greatest possible = 109 (Just less than 1)

Answer = D
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Re: The average (arithmetic mean) of 4 positive integers is 50.  [#permalink]

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New post 12 Dec 2016, 10:46
Sum(4)=200
Sum(2)=90
Hence um(2 leftovers)=200-90=110

Since there is no restriction of the median
Let one of them be 1 => other one will be 109

Hence D
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Re: The average (arithmetic mean) of 4 positive integers is 50.  [#permalink]

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New post 30 Jan 2017, 15:31
Bunuel wrote:
iyersu wrote:
The average (arithmetic mean) of 4 positive integers is 50. If the average of 2 of these integers is 45, what is the greatest possible value that one of the other 2 integers can have?

A. 55
B. 65
C. 100
D. 109
E. 115


The sum of 4 integers is 4*50 = 200.
The sum of 2 integers is 2*45 = 90.

Thus, the sum of the other 2 integers is 200 - 90 = 110. Since we know that the integers are positive then the greatest one from these two can be 109, the other one being 1.

Answer: D.

Hope it's clear.


Sorry I do not understand why sum of two remaining integers = 110 becomes 109?
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Re: The average (arithmetic mean) of 4 positive integers is 50.  [#permalink]

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New post 31 Jan 2017, 09:55
kanusha wrote:
Bunuel wrote:
iyersu wrote:
The average (arithmetic mean) of 4 positive integers is 50. If the average of 2 of these integers is 45, what is the greatest possible value that one of the other 2 integers can have?

A. 55
B. 65
C. 100
D. 109
E. 115


The sum of 4 integers is 4*50 = 200.
The sum of 2 integers is 2*45 = 90.

Thus, the sum of the other 2 integers is 200 - 90 = 110. Since we know that the integers are positive then the greatest one from these two can be 109, the other one being 1.

Answer: D.

Hope it's clear.


Sorry I do not understand why sum of two remaining integers = 110 becomes 109?


x + y = 110, where both x and y are positive integers. The max value of say x there is 109, when y = 1.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: The average (arithmetic mean) of 4 positive integers is 50.  [#permalink]

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Re: The average (arithmetic mean) of 4 positive integers is 50. &nbs [#permalink] 27 Nov 2018, 10:20
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