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Is x a multiple of 4?

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Is x a multiple of 4?  [#permalink]

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New post 22 Sep 2019, 07:34
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Is x a multiple of 4?

(1) x + 2 is divisible by 2

(2) 6 is a factor of 3x
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Re: Is x a multiple of 4?  [#permalink]

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New post 22 Sep 2019, 08:42
1
AS0306 wrote:
Is x a multiple of 4?

(1) x + 2 is divisible by 2

(2) 6 is a factor of 3x

Dear! This question is for data sufficiency section.

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Re: Is x a multiple of 4?  [#permalink]

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New post 22 Sep 2019, 08:52
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Re: Is x a multiple of 4?  [#permalink]

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New post 22 Sep 2019, 09:11
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AS0306 wrote:
Is x a multiple of 4?

(1) x + 2 is divisible by 2

(2) 6 is a factor of 3x


\(\frac{x}{4}\)=integer?

(1) x + 2 is divisible by 2

\(\frac{x+2}{2}\)=integer =>x=2, 4, 6, 8....(all multiples of 2)

If x=2, is \(\frac{2}{4}\)=integer? NO

If x=4, is \(\frac{4}{4}\)=integer? YES

If x=6, is \(\frac{6}{4}\)=integer? NO

INSUFFICIENT!

(2) 6 is a factor of 3x

\(\frac{3x}{6}\)= integer => \(\frac{x}{2}\) = integer =>x=2, 4, 6, 8....(all multiples of 2)

If x=2, is \(\frac{2}{4}\)=integer? NO

If x=4, is \(\frac{4}{4}\)=integer? YES

If x=6, is \(\frac{6}{4}\)=integer? NO

INSUFFICIENT!

(1) + (2)

\(\frac{x+2}{2}\)=integer and \(\frac{x}{2}\) = integer.........Same as individual statements...no extra information
INSUFFICIENT!

Hence, answer is option E.

P.S: Please check the OA since it says the answer is option C

Bunuel please help confirm the OA
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Re: Is x a multiple of 4?  [#permalink]

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New post 24 Sep 2019, 21:48
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EncounterGMAT wrote:
AS0306 wrote:
Is x a multiple of 4?

(1) x + 2 is divisible by 2

(2) 6 is a factor of 3x


\(\frac{x}{4}\)=integer?

(1) x + 2 is divisible by 2

\(\frac{x+2}{2}\)=integer =>x=2, 4, 6, 8....(all multiples of 2)

If x=2, is \(\frac{2}{4}\)=integer? NO

If x=4, is \(\frac{4}{4}\)=integer? YES

If x=6, is \(\frac{6}{4}\)=integer? NO

INSUFFICIENT!

(2) 6 is a factor of 3x

\(\frac{3x}{6}\)= integer => \(\frac{x}{2}\) = integer =>x=2, 4, 6, 8....(all multiples of 2)

If x=2, is \(\frac{2}{4}\)=integer? NO

If x=4, is \(\frac{4}{4}\)=integer? YES

If x=6, is \(\frac{6}{4}\)=integer? NO

INSUFFICIENT!

(1) + (2)

\(\frac{x+2}{2}\)=integer and \(\frac{x}{2}\) = integer.........Same as individual statements...no extra information
INSUFFICIENT!

Hence, answer is option E.

P.S: Please check the OA since it says the answer is option C

Bunuel please help confirm the OA


You are right. Correct answer is E. Edited. Thank you.
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Re: Is x a multiple of 4?  [#permalink]

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New post 03 Nov 2019, 11:51
Can somebody explain to me why if 6 is a factor of 3x, than x must be divisible by 2?
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Re: Is x a multiple of 4?  [#permalink]

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New post 27 Nov 2019, 16:22
whollymoses wrote:
Can somebody explain to me why if 6 is a factor of 3x, than x must be divisible by 2?



whollymoses
Well, if 6 is a factor of 3x then the least value x can take is 2. Because then 3x becomes 6 and 6 is a factor of 6. The next value x can take is 4, which gives us 12 and 6 is a factor of 12. And So on.

I hope that helps!
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Re: Is x a multiple of 4?  [#permalink]

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New post 27 Nov 2019, 18:23
AS0306 wrote:
Is x a multiple of 4?

(1) x + 2 is divisible by 2

(2) 6 is a factor of 3x


(1) X could be 0 or 2, in this case X will not be a multiple of 4. X could be 4 or 8, which are multiples of 4. Not sufficient.

(2) 3x/6 = an integer. x can be 2, 4 or 6, so it may or may not be a multiple of 4. Not sufficient.

Together, X can be 6 or 10, or 4 or 8. Not sufficient.

E is the answer.
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Re: Is x a multiple of 4?  [#permalink]

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New post 27 Nov 2019, 23:37
AS0306 wrote:
Is x a multiple of 4?

(1) x + 2 is divisible by 2

(2) 6 is a factor of 3x


The individual statements are not enough and give the same information that x is divisible by 2. If x is divisible by 2, it does not mean that it is also divisible by 4; it may or may not be the case.

Hence the correct answer is option E
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Re: Is x a multiple of 4?   [#permalink] 27 Nov 2019, 23:37
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