quick question on divisibility - need expert help

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If X is divisible by 2, we say that the number is "Even." However, "even" implies that the number is an integer. On the other hand, X could be 12.2, which is also divisible by 2 and not an integer. Is it fair to say that when "x is divisible by 2" => it doesn't necessarily mean that the number will be an integer?

Please help.

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by Shalabh's Quants » Mon Apr 23, 2012 4:18 am
voodoo_child wrote:If X is divisible by 2, we say that the number is "Even." However, "even" implies that the number is an integer. On the other hand, X could be 12.2, which is also divisible by 2 and not an integer. Is it fair to say that when "x is divisible by 2" => it doesn't necessarily mean that the number will be an integer?

Please help.
It should be...'An integer number X divisible by 2 is Even.'
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by [email protected] » Mon Apr 23, 2012 4:50 am
Even itself mean that it is an integer i.e set of even numbers and odd numbers is the subset of set of integers. Hence we don't check the divisibility of non integers.

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by neelgandham » Mon Apr 23, 2012 4:55 am
Is it fair to say that when "x is divisible by 2" => it doesn't necessarily mean that the number will be an integer?
To answer your question quoted, Yes it is absolutely correct to assume that x isn't necessarily an integer in this case.

Given the same statements, the answer to the question If x is positive. Is x divisible by 2 ? is not the same as the answer to the question If integer x is positive. Is x divisible by 2?. In my opinion, the later is a more GMATty question.
(1) x^3+x is divisible by 4
(2) 5x+4 is divisible by 6

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by [email protected] » Mon Apr 23, 2012 6:43 am
In my experience, I thinks it's safe to say that the GMAT won't use the term "divisible" (e.g., "K is divisible by n") without first specifying that the numbers involved are integers.

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by Mr Smith » Mon Apr 23, 2012 8:32 am
Hey voodoo_child,

First Your argument that 12.2 is divisible by 2 is incorrect because: The concept of divisibility is used only for integers as correctly indicated by happyurfriendly. And a number being divisible by definition means would result in no remainder AND an integral quotient. So it is incorrect because for one 12.2 is not an integer, and 2nd 12.2 /2 = 6.1 which is not an integer.

In simpler terms, kindly remember that divisibility is always tested of integers only. Use the following definition of divisibility for clarity.

An INTEGER when divided by another INTEGER results in a quotient which is also an INTEGER and a Zero remainder, then the 1st integer is said to be DIVISIBLE by the second.
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by Abhishek009 » Mon Apr 23, 2012 9:16 am
voodoo_child wrote:If X is divisible by 2, we say that the number is "Even." However, "even" implies that the number is an integer. On the other hand, X could be 12.2, which is also divisible by 2 and not an integer. Is it fair to say that when "x is divisible by 2" => it doesn't necessarily mean that the number will be an integer?

Please help.
Consider this in the simplest way -

Any number which can be arranged in rows & ( Or ) column can be called an even number.


Say 2{2 Columns 1 Row }

o o

Say 4 { 2 columns 2 rows }

o o

o o

Say 6 {2 Columns 3 rows or 3 Columns 2 Rows }

o o o o o
Or o o
o o o 0 0


Now 12.2 doesn't follow the said rule , hence it can't be called an even number...
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by [email protected] » Tue Apr 24, 2012 3:54 pm
hey, voodoo_child what explanation Mr. Smith gave is perfectly correct. That is the correct meaning of the term 'Divisibility'.

When I say that any term is perfectly divisible by some other term, I mean that the quotient is a natural number or whole number. Hence an integer. It can never be a decimal fraction or decimal.

It has to be perfectly divisible.

So when you have the number 12.2 which is already is a decimal fraction, is divided by 2, still it is not perfectly divisible by 2 as the quotient is not an integer.

Supposedly, the number is 7.5 and if it is divided by 1.5, then the quotient is 5 (an integer).

In this case, you can say that 7.5 is divisible by 1.5.

You could also say that the given number should be perfectly divisible by the divisor.

Hope the above examples will help you...
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