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# Is a divisible by 3?

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Math Expert
Joined: 02 Aug 2009
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Is a divisible by 3? [#permalink]

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04 Jan 2018, 09:15
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Is $$a$$ divisible by $$3$$?

(1) $$a+3b$$ is divisible by $$3$$.
(2) $$b$$ is divisible by $$3$$.

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[Reveal] Spoiler: OA

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Manager
Joined: 23 Feb 2017
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Re: Is a divisible by 3? [#permalink]

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04 Jan 2018, 10:46
Ans A

Statement 1 a+3b is divisible by 3.

3b will be multiple of 3 so as a.

sufficient

Statement 2 b is divisible by 3.
we don't know about a
not sufficient
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Re: Is a divisible by 3? [#permalink]

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04 Jan 2018, 11:16
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chetan2u wrote:
Is $$a$$ divisible by $$3$$?

(1) $$a+3b$$ is divisible by $$3$$.
(2) $$b$$ is divisible by $$3$$.

New Question

Here we are NOT given that a/b are integers, so we cannot assume them to be so.

(1) a+3b is divisible by 3. If b =2/3, this makes 3b = 2. Now we can have a = 1, which makes a+3b divisible by 3, and here 'a' is NOT divisible by 3.
But we can have another case say b = 1, here 3b = 3. Now whichever value a takes will have to be a multiple of 3 (eg, 3, 6,..) in order for a+3b to be a multiple of 3.
So 'a' can or cannot be a multiple of 3. Not sufficient.

(2) This doesnt tell anything about 'a', so definitely Not Sufficient.

Combining the two statements, since b is divisible by 3, b has to be an integer. So 3b will also definitely be an integer. Now a+3b is also divisible by 3 and 3b is divisible by 3..this can only happen if 'a' too is divisible by 3. Sufficient.

Hence C answer
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Re: Is a divisible by 3? [#permalink]

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04 Jan 2018, 23:18
chetan2u wrote:
Is $$a$$ divisible by $$3$$?

(1) $$a+3b$$ is divisible by $$3$$.
(2) $$b$$ is divisible by $$3$$.

New Question

Hi Can any body explain the error in my solution please.
Statement 1
a+3b is divisible by 3 that means a+3b=3x where x is some number
now a=3x-3b
a=3*(x-b) thus it is divisible by 3 hence sufficient .
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Re: Is a divisible by 3? [#permalink]

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04 Jan 2018, 23:48
arvind910619 wrote:
chetan2u wrote:
Is $$a$$ divisible by $$3$$?

(1) $$a+3b$$ is divisible by $$3$$.
(2) $$b$$ is divisible by $$3$$.

New Question

Hi Can any body explain the error in my solution please.
Statement 1
a+3b is divisible by 3 that means a+3b=3x where x is some number
now a=3x-3b
a=3*(x-b) thus it is divisible by 3 hence sufficient .

it is because a or b can still be non-integer numbers.

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Senior Manager
Joined: 02 Apr 2014
Posts: 470
Re: Is a divisible by 3? [#permalink]

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22 Jan 2018, 22:56
Good tricky question this.

Statement 1:
if b integer, a + 3b is divisble by 3 => a is divisible by 3
but if b = 1/3, say a = 2, then 2 + 3(1/3) = 3 is divisible by 3, but a = 2 not divisible by 3.

InSuff

Statement 2: clearly insuff

from (1)+(2) , b is not integer, so a has to multiple of 3 => (C)
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Re: Is a divisible by 3? [#permalink]

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27 Jan 2018, 16:17
Why does “B is divisible by 3” necessarily mean that B is an integer? B could be 3.9 and be divisible by 3. It would yield 1.3. Wouldn’t that be correct?

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Re: Is a divisible by 3? [#permalink]

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27 Jan 2018, 20:18
Rurugu wrote:
Why does “B is divisible by 3” necessarily mean that B is an integer? B could be 3.9 and be divisible by 3. It would yield 1.3. Wouldn’t that be correct?

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Hi Rurugu

you get a decimal number only when that integer is not divisible by another integer. For eg. if you divide 5 by 2 then you will get 2.5. 5 when divided by 2 leaves 1 as remainder and that remainder is converted into decimal form.

In your example 3.9=39/10 which will not be divisible by 3.
Math Expert
Joined: 02 Sep 2009
Posts: 44636
Re: Is a divisible by 3? [#permalink]

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28 Jan 2018, 00:10
Rurugu wrote:
Why does “B is divisible by 3” necessarily mean that B is an integer? B could be 3.9 and be divisible by 3. It would yield 1.3. Wouldn’t that be correct?

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On GMAT when we are told that $$a$$ is divisible by $$b$$ (or which is the same: "$$a$$ is multiple of $$b$$", or "$$b$$ is a factor of $$a$$"), we can say that:
1. $$a$$ is an integer;
2. $$b$$ is an integer;
3. $$\frac{a}{b}=integer$$.

Though, still a and b being (positive) integers still would be mentioned.
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Re: Is a divisible by 3? [#permalink]

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26 Feb 2018, 03:55
In this question, when combining 1) and 2) could not a=0? Hence answer should be E?
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Re: Is a divisible by 3? [#permalink]

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26 Feb 2018, 04:11
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ma123 wrote:
In this question, when combining 1) and 2) could not a=0? Hence answer should be E?

Hi ma123

if a=0, then it will automatically be divisible by 3. 0 is divisible by every number. 0/3=0
Re: Is a divisible by 3?   [#permalink] 26 Feb 2018, 04:11
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# Is a divisible by 3?

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