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If x is a positive integer, does 6 divide evenly into x?

(1) 3x/6 is an integer. (2) 11x/6 is an integer.

Very important to keep a track of number properties..

does 6 divide evenly into x MEANS "is X a multiple of 6 ?,

lets see the statements

(1) 3x/6 is an integer. we can just be sure that x is an even integer... as there is 3 in nummerator and denominator, we cannot say anything about div by3.. x = 4, 3x/6 = 12/6 = 2 .. ans NO x=12 , 3x/6=36/6=6.. ans YES Insuff

(2) 11x/6 is an integer since Both 6 and 11 are CO_PRIMES, x has to be a multiple of 6 for 11x/6 to be an integer Suff

Re: If x is a positive integer, does 6 divide evenly into x? [#permalink]

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19 Apr 2016, 14:54

Let's evaluate each statement to check whether 6 is a factor of x

(1) 3x/6 is an integer. This means x/2 is an integer. Which tells us basically x can be any even number and the statement holds true. Try x as 4, 6, 8 ,12, 14. So, Statement 1 can pinpoint a specific value for x for which it may or may not be divisible by 6 Not Sufficient on its own

(2) 11x/6 is an integer. This tells us that the number x has to be a multiple of 6 as any number multiplied by a co-prime of 6 can only be divisible of 6 if it is a multiple of 6

If x is a positive integer, does 6 divide evenly into x? [#permalink]

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19 Apr 2016, 20:39

chetan2u wrote:

does 6 divide evenly into x MEANS '"is X a multiple of 6 ?,

I solved the entire Q assuming that this statement means ' is X a factor of 6'

6 divides evenly into x --> Isn't this the same as stating '6 chocolates divide evenly into x children'?

If yes, x should either be 2 or 3 (ignoring 1 intentionally).

So, shouldn't the statement mean X is a factor of 6?

If x were to be a multiple of 6, wouldn't the statement be '6 divides x evenly'?

PS: I know I am a little confused about the use of language in this Q, but any help in pointing out where I am going wrong would be greatly appreciated!

does 6 divide evenly into x MEANS '"is X a multiple of 6 ?,

I solved the entire Q assuming that this statement means ' is X a factor of 6'

6 divides evenly into x --> Isn't this the same as stating '6 chocolates divide evenly into x children'?

If yes, x should either be 2 or 3 (ignoring 1 intentionally).

So, shouldn't the statement mean X a factor of 6?

If x were to be a multiple of 6, wouldn't the statement be '6 divides x evenly'?

PS: I know I am a little confused about the use of language in this Q, but any help in pointing out where I am going wrong would be greatly appreciated!

Hi, If I talk of example of chocolates and kids.. we say 6 cocolates are evenly distributed in kids.. this will mean number of kids is a factor of number of chocolates.. OR I would say divide 6 chocolates evenly into kids, meaning the same as above.. But 6 chocolates divide evenly into x children may not be correct..

Now what Q asks us "6 divides evenly into x " MEANS x/6 is an integer.. x/6 as an integer means x is a multiple of 6..

say I remove some words from "does 6 divide evenly into x"-- does 6 divide evenly into x-- In a way you get that " Is 6 a factor of x?"
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Re: If x is a positive integer, does 6 divide evenly into x? [#permalink]

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28 Aug 2017, 09:07

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