A, B are integers and AB is divisible by 12, Is A divisible by 6 ?

Question

A, B are integers and AB is divisible by 12, is A divisible by 6 ?

(1) A/B is divisible by 3.

(2) B is divisible by 4.

confused with this question, can someone please help ?

Bunuel  please help I'm confused in A and D.

RAHULSAINI · Answer

How I solved is 
We have given A and B are integers 
That means A, B can be +ve -ve or 0

And AB is divisible by 12 means we have remainder as 0

So AB =12Q
Where Q is quotient

From 1st we have
A/B = 3Q as Remainder is 0.

So 12 Q = 4A/B

When we put value in given
We get A=0 B=+-2

Our question is A divisible by 0
We get yes
So sufficient

In second
B= 4Q 
So 12 Q = 3B
when we put it in given 
We get B=0 and A=3

Our question is A=3 divided by 6
NO

sufficient as we get definite answer

Pls let me know where I'm wrong

chetan2u · Answer

hi rahul,

i think ans should be A,...
1) A/B is divisible by 3.... this means A=3BX, where X can be 1,2,3...
but B is a subset of A... so A will surely be divisible by 2also as AB is div by 12...
sufficient as A is div by both A and B...
2) B is div by 4... B can be div by 12.. Also A can be divisible by 12 or 24...
it is nowhere mentioned that AB is div by only 12.. it can be divisible by even 24, 50 etc..
we just know that AB has atleast 12 as factor.. nothing more... insufficient

ans A

Bunuel · Answer

A, B are integers and AB is divisible by 12, Is A divisible by 6 ?

AB is divisible by 12 means that AB can be ..., -12, 0, 12, 24, ... Notice that for AB to be even (a multiple of 12) either A or B (or both) must be even.

(1) A/B is divisible by 3 --> A/B = 3k --> A = B*3k, so A is a multiple of 3.

If A is even, then A is a multiple of 2 and 3, so a multiple of 6.
If B is even, then A = B*3k = even*3k = so a multiple of 6.

So, in any case A must be a multiple of 6. Sufficient.

(2) B is divisible by 4. If B = 12 and A = 1, then the answer is NO but if B = 12 and A = 6, then the answer is YES. Not sufficient.

Answer: A.

AdlaT · Answer

A and B are integers and AB/12=k(k is an integer) , is A/6 an integer?

St: 1)  \frac{A}{B}=3*t

A=3*B*t
 
  A=3*(\frac{12K}{A})*t

A^2= 36* t*K

A=6*(something)

Clearly A is divisible by 6, so SUFFICIENT.

St:2) B=4t, and We know  A=\frac{12k}{B}=\frac{12k}{4t}=3*(k/t)

A=3*(\frac{k}{t})

IF k=t then A is NOT DIVISIBLE BY 6 and IF k=2t then A is DIVISIBLE BY 6.

SO NOT SUFFICEINT.

ANS: A

A, B are integers and AB is divisible by 12, Is A divisible by 6 ?

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