Is the integer b divisible by 3 ?

Question

Is the integer b divisible by 3 ?
 
(1) 8b is divisible by 6.
 
(2) 9b is divisible by 12.

nalinnair · Answer

Given b is an integer.

Statement 1
8b is divisible by 6
Since 8 comprises of 2's, b must be a multiple of 3. Hence, this is sufficient.

Statement 2
9b is divisible by 12
if b = 4 then 9b = 36 (which is divisible by 12), b is not divisible by 3
if b = 12 then 9b = 108 (which is divisible by 12), b is divisible by 3
Hence, insufficient

Answer - A

adiagr · Answer

Statement 1

8 and 6 have 2 as highest common factor. So b will have to be divisible by 3. Sufficient.

Statement 2 
 
9 and 12 have 3 as highest common factor. So b will be divisible by (4). 
so this statement does not tell me that b is divisible by 3. Not sufficient.

So only first statement is sufficient.

Answer: A

Tan2017 · Answer

Statement 1: Considering 8 is divisible by 2, in order for 8b to be divisible by 6, b needs to be divisible by 3. Hence Sufficient. 
Statement 2: Since 9b is already divisible by 3, b may or may not be divisible by 3. Not sufficient.

shekyonline · Answer

Statement 1: 8b : If it is to divisible by 6 , it has to have factors (3 and 2). 8 can provide factor of 2, not 3. So, b has to have factor of 3. SUFFICIENT.

Statement 2: 9*b : 9 has 3*3; b need not have factor of 3 for 9*b to be divisible by 12.

not SUFFICIENT.

Ans. - A

fskilnik · Answer

b\,\,\operatorname{int}

\frac{b}{3}\,\,\mathop = \limits^? \,\,\operatorname{int}

\left( 1 ight)\,\,\frac{{4b}}{3}\,\, = \,\,\,\operatorname{int} \,\,\,\,\mathop \Rightarrow \limits^{GCD\left( {3,4} ight)\,\, = \,\,1} \,\,\,\frac{b}{3} = \operatorname{int} \,\,\,\, \Rightarrow \,\,\,\left\langle {{	ext{YES}}} ightangle

\left( 2 ight)\,\,\frac{{3b}}{4}\,\, = \,\,\,\operatorname{int} \,\,\,\,\left\{ \begin{gathered}
 \,{	ext{Take}}\,\,b = 0\,\,\,\, \Rightarrow \,\,\,\left\langle {{	ext{YES}}} ightangle \hfill \
 \,{	ext{Take}}\,\,b = 4\,\,\,\, \Rightarrow \,\,\,\left\langle {{	ext{NO}}} ightangle \hfill \ 
\end{gathered} ight.

This solution follows the notations and rationale taught in the GMATH method.

TestPrepUnlimited · Answer

Statement 1: 
4b is divisible by 3. The factor of 3 can come from either 4 or b, since 3 is not a factor of 4 it must be a factor of b. Therefore b is divisible by 3. Sufficient.

Statement 2: 
3b is divisible by 4. Again from the logic above, b has a factor of 4 but we still don't know if it has a factor of 3. Insufficient.

Ans: A

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Is the integer b divisible by 3 ?

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