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What is the greatest integer that will always evenly divide the sum of

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Bunuel
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What is the greatest integer that will always evenly divide the sum of [#permalink] New post   04 Dec 2015, 00:54
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What is the greatest integer that will always evenly divide the sum of three consecutive even integers?

A. 2
B. 3
C. 4
D. 6
E. 12
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Re: What is the greatest integer that will always evenly divide the sum of [#permalink] New post   04 Dec 2015, 01:57
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Let the three consecutive even integers be 2x , 2x + 2 , 2x + 4
Sum = 2x + 2x + 2 + 2x + 4
= 6x+6 = 6(x+1)
Therefore , 6 will always be a factor .

Answer D
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Re: What is the greatest integer that will always evenly divide the sum of [#permalink] New post   05 Dec 2015, 04:10
Skywalker18 wrote:
Let the three consecutive even integers be 2x , 2x + 2 , 2x + 4
Sum = 2x + 2x + 2 + 2x + 4
= 6x+6 = 6(x+1)
Therefore , 6 will always be a factor .

Answer D



Take an example 4+6+8
sum=18 and 18/6=3,is 3 even?

ans should be obtion B
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Re: What is the greatest integer that will always evenly divide the sum of [#permalink] New post   05 Dec 2015, 04:35
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RatneshS wrote:
Skywalker18 wrote:
Let the three consecutive even integers be 2x , 2x + 2 , 2x + 4
Sum = 2x + 2x + 2 + 2x + 4
= 6x+6 = 6(x+1)
Therefore , 6 will always be a factor .

Answer D



Take an example 4+6+8
sum=18 and 18/6=3,is 3 even?

ans should be obtion B


Hi RatneshS ,
The term evenly divisible means that the process of division should result in a remainder of 0 .
It does not mean that the quotient of the division should be an even number .
Hope it helps!! :)
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Re: What is the greatest integer that will always evenly divide the sum of [#permalink] New post   09 Jan 2021, 09:07
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Bunuel wrote:
What is the greatest integer that will always evenly divide the sum of three consecutive even integers?

A. 2
B. 3
C. 4
D. 6
E. 12


The consecutive even integers can be taken as 2a-2, 2a, 2a+2.
Sum = \(2a-2 + 2a+ 2a+2=6a\).

Now a can be ANY integer, so we cannot be sure of the factors of a.
But 6a is surely divisible by 6.

D

NOTE : There is always a query on 'evenly divisible'. 'Evenly divisible' means completely divisible, that is the answer is an integer and not a decimal. Do not mistake it for even numbers.
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Re: What is the greatest integer that will always evenly divide the sum of [#permalink]
09 Jan 2021, 09:07
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