Is a divisible by 3?

Question

Is  a  divisible by  3 ?

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

mandeey · Answer

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

amanvermagmat · Answer

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

arvind910619 · Answer

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 .

chesstitans · Answer

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

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hellosanthosh2k2 · Answer

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)

Rurugu · Answer

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

niks18 · Answer

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.

Bunuel · Answer

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.

ma123 · Answer

In this question, when combining 1) and 2) could not a=0? Hence answer should be E?

niks18 · Answer

Hi  ma123

if a=0, then it will automatically be divisible by 3. 0 is divisible by every number. 0/3=0

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Is a divisible by 3?

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