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

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iyersu

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

Updated on: 21 Dec 2013, 04:05

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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

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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]

21 Dec 2013, 04:16

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Expert Reply

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]

10 Sep 2014, 22:01

1

Kudos

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]

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]

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]

31 Jan 2017, 09:55

Expert Reply

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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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. [#permalink]

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