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Is a divisible by 3?

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Is a divisible by 3? [#permalink]

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New post 04 Jan 2018, 08:15
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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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Re: Is a divisible by 3? [#permalink]

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New post 04 Jan 2018, 09:46
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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New post 04 Jan 2018, 10:16
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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New post 04 Jan 2018, 22:18
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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Is a divisible by 3? [#permalink]

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New post 04 Jan 2018, 22:48
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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Is a divisible by 3?   [#permalink] 04 Jan 2018, 22:48
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