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Manager  Joined: 11 Jan 2008
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Is the integer x divisible by 6?  [#permalink]

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Difficulty:   35% (medium)

Question Stats: 67% (01:27) correct 33% (01:23) wrong based on 1033 sessions

### HideShow timer Statistics Is the integer x divisible by 6?

(1) x + 3 is divisible by 3
(2) x + 3 is an odd number

I get C.
As, say x = 6.
x+3 = 9 which is odd and divisible by 3.

But what is we put in x as "0".
x + 3 is 3 which is also odd and divisible by 3 but not 6.

Any idea what am I missing?

Originally posted by jackychamp on 14 Feb 2008, 12:37.
Last edited by Bunuel on 12 Jun 2014, 11:19, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
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Re: Is the integer x divisible by 6?  [#permalink]

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Is the integer x divisible by 6?

(1) x + 3 is divisible by 3. This basically means that x is divisible by 3 (x = {a multiple of 3} - 3 = {a multiple of 3}), which is not sufficient to say whether it's divisible by 6.

(2) x + 3 is an odd number. This means that x is even ($$x=odd-3=odd-odd=even$$). Not sufficient.

(1)+(2) x is an even multiple of 3, hence it's a multiple of 6. Sufficient.

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Is the integer x divisible by 6?  [#permalink]

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Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and equations ensures a solution.

Is the integer x divisible by 6?

(1) x + 3 is divisible by 3
(2) x + 3 is an odd number

In the original condition there is 1 variable and we need 1 equation to match the number of variable and equation. Since there is 1 each in 1) and 2), D is likely the answer.

In case of 1), x+3=3t(t:some integer) thus x=multiple of 3. If x=3 the answer is no, if x=6 the answer is yes. Therefore the condition is not sufficient.
In case of 2), if x+3=odd, x=odd-3=even, x=2 then the answer is no. If x=6 the answre is yes, therefore the condition is not sufficient.
Using both 1) & 2) together, if x=multiple of 3 and even, it must be a multiple of 6 and thus the answer is yes. Therefore the answer is C.
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Re: Is the integer x divisible by 6?  [#permalink]

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Bunuel : If x = 0 (which is an even no.) + 3 is divisible by 3.
But 0/6 is not divisible. Am i missing something?
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Re: Is the integer x divisible by 6?  [#permalink]

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Vishvesh88 wrote:
Bunuel : If x = 0 (which is an even no.) + 3 is divisible by 3.
But 0/6 is not divisible. Am i missing something?

0/6 = 0 = integer. 0 is divisible by every integer except 0 itself.
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Re: Is the integer x divisible by 6?  [#permalink]

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Bunuel : Muchos Gracias Bunuel.
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Re: Is the integer x divisible by 6?  [#permalink]

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jackychamp wrote:
Is the integer x divisible by 6?

(1) x + 3 is divisible by 3
(2) x + 3 is an odd number

We need to determine whether x/6 = integer.

Statement One Alone:

x + 3 is divisible by 3.

Statement one is not sufficient to answer the question. If x = 3, then x is not divisible by 6; however, if x = 6, then x is divisible by 6.

Statement Two Alone:

x + 3 is an odd number.

Statement two is not sufficient to answer the question. If x = 2, then x is not divisible by 6; however, if x = 6, then x is divisible by 6.

Statements One and Two Together:

Using statements one and two, we see that x + 3 is an odd multiple of 3, such as 3, 9, 15, etc. Thus, x must be an even multiple of 3. Since all even multiples of 3 are multiples of 6, x/6 is an integer.

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Re: Is the integer x divisible by 6?  [#permalink]

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Bunuel wrote:
Is the integer x divisible by 6?

(1) x + 3 is divisible by 3. This basically means that x is divisible by 3 (x = {a multiple of 3} - 3 = {a multiple of 3}), which is not sufficient to say whether it's divisible by 6.

(2) x + 3 is an odd number. This means that x is even ($$x=odd-3=odd-odd=even$$). Not sufficient.

(1)+(2) x is an even multiple of 3, hence it's a multiple of 6. Sufficient.

Hi Bunuel, Do we need to consider negative integer for statement (1)?
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Re: Is the integer x divisible by 6?  [#permalink]

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hazelnut wrote:
Bunuel wrote:
Is the integer x divisible by 6?

(1) x + 3 is divisible by 3. This basically means that x is divisible by 3 (x = {a multiple of 3} - 3 = {a multiple of 3}), which is not sufficient to say whether it's divisible by 6.

(2) x + 3 is an odd number. This means that x is even ($$x=odd-3=odd-odd=even$$). Not sufficient.

(1)+(2) x is an even multiple of 3, hence it's a multiple of 6. Sufficient.

Hi Bunuel, Do we need to consider negative integer for statement (1)?

x could be a negative integer for (1) or/and (2) but it does not affect the answer. For example, when we consider the statements together, we get that x is an even multiple of 3, so x could be ..., -12, -6, 0, 6, 12, ... As you can see x is indeed divisible by 6 for all possible values of x.
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Re: Is the integer x divisible by 6?  [#permalink]

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I have a doubt regarding this question because as per my approach I got answer D.

The question says x is divisible by 6 which means x can be 6,12,18,24 ......etc

Stat1: x+3 is divisible by 3
We plug in any value of x, say 12, so 12+3=15 which is divisible by 3. Likewise, put in the rest of the numbers. Sufficient.

Stat2: x+3 is an odd number.
We know any even+odd=odd so all the values are even for x so plugging in here we can prove that x+3 is indeed odd. Sufficient.

Where am I going wrong?

Posted from my mobile device
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Re: Is the integer x divisible by 6?  [#permalink]

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Whenever you see a data sufficiency question, its a good idea to ask yourself, "What would I need to know in order to answer this question?" Stated differently, its a good idea to ask yourself, "What's the question behind the question?" Doing so will get your mental juices flowing before you take a look at the statements...

The question here is whether x is divisible by 6. The question behind the question is, "Is x divisible by both 2 and 3?" That's what you'd need to know in order to answer the original question. With that in mind, you know what to look for when you take a look at the two statements, so when you read in statement (1) that x + 3 is divisible by 3, it may pop out at you quickly that, "Oh, yes, so that means x itself is divisible by 3. Statement (1) isn't sufficient, but it does tell me half of what I need to know."

Same story for statement (2). When you see that x + 3 is odd, you may recall quickly that x must be EVEN - i.e. x is divisible by 2 - and you'll think, "Great. That's the second half of what I need to know. Answer C."
_________________ Re: Is the integer x divisible by 6?   [#permalink] 23 Nov 2018, 18:44
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