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

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Is the integer b divisible by 3 ?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

Is the integer b divisible by 3 ?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards