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Is a divisible by 3?

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Is a divisible by 3? [#permalink]

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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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Re: Is a divisible by 3? [#permalink]

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New post 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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chetan2u wrote:
Is \(a\) divisible by \(3\)?

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

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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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New post 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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New post 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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Re: Is a divisible by 3? [#permalink]

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New post 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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New post 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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New post 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.
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Re: Is a divisible by 3? [#permalink]

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New post 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?

Posted from my mobile device


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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New post 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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New post 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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