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

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Bunuel
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If x is a positive integer, does 6 divide evenly into x? [#permalink] New post   19 Apr 2016, 03:11
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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.
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B
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chetan2u
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Re: If x is a positive integer, does 6 divide evenly into x? [#permalink] New post   19 Apr 2016, 08:01
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Bunuel wrote:
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

B
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Re: If x is a positive integer, does 6 divide evenly into x? [#permalink] New post   19 Apr 2016, 15:54
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

So Statement 2 is Sufficient

Correct Option : B
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If x is a positive integer, does 6 divide evenly into x? [#permalink] New post   19 Apr 2016, 21:39
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! :)
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Re: If x is a positive integer, does 6 divide evenly into x? [#permalink] New post   19 Apr 2016, 21:55
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bikographer wrote:
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 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] New post   20 Apr 2016, 07:58
you yrself are saying wrong

6 chocs and 2 children, then yes 6 chocs can be divided equally among 2

but if 6 chocs and 24 children, then no, 6 choch can not be divided among 24 chilren(given fractions are avoided)

so x/6 is what we are looking for
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Re: If x is a positive integer, does 6 divide evenly into x? [#permalink] New post   28 Jun 2020, 14:05
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Bunuel wrote:
If x is a positive integer, does 6 divide evenly into x?

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


This is the same as asking if x has a factor of 6.

Statement 1:

This simplifies to x/2 is an integer. Then we know x is even, but that doesn't necessarily mean x is divisible by 6. Insufficient.

Statement 2:

(11x)/6 is an integer. The factor of 6 cannot come from 11, therefore it must have been taken out of x. Then x/6 must be an integer. Hence x has a factor of 6. Sufficient.

Ans: B
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Re: If x is a positive integer, does 6 divide evenly into x? [#permalink]
28 Jun 2020, 14:05
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