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Is the integer b divisible by 3 ?

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Math Expert
Joined: 02 Sep 2009
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Is the integer b divisible by 3 ?  [#permalink]

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26 May 2016, 11:14
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35% (medium)

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66% (01:07) correct 34% (01:13) wrong based on 226 sessions

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Is the integer b divisible by 3 ?

(1) 8b is divisible by 6.

(2) 9b is divisible by 12.

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Re: Is the integer b divisible by 3 ?  [#permalink]

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26 May 2016, 20:38
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Bunuel wrote:
Is the integer b divisible by 3 ?

(1) 8b is divisible by 6.

(2) 9b is divisible by 12.

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

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Re: Is the integer b divisible by 3 ?  [#permalink]

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27 May 2016, 01:37
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.

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Is the integer b divisible by 3 ?  [#permalink]

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16 Mar 2017, 19:40
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.
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Is the integer b divisible by 3 ?  [#permalink]

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19 Mar 2017, 10:57
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
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Re: Is the integer b divisible by 3 ?  [#permalink]

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04 Sep 2018, 11:44
Bunuel wrote:
Is the integer b divisible by 3 ?

(1) 8b is divisible by 6.

(2) 9b is divisible by 12.

$$b\,\,\operatorname{int}$$

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

$$\left( 1 \right)\,\,\frac{{4b}}{3}\,\, = \,\,\,\operatorname{int} \,\,\,\,\mathop \Rightarrow \limits^{GCD\left( {3,4} \right)\,\, = \,\,1} \,\,\,\frac{b}{3} = \operatorname{int} \,\,\,\, \Rightarrow \,\,\,\left\langle {{\text{YES}}} \right\rangle$$

$$\left( 2 \right)\,\,\frac{{3b}}{4}\,\, = \,\,\,\operatorname{int} \,\,\,\,\left\{ \begin{gathered} \,{\text{Take}}\,\,b = 0\,\,\,\, \Rightarrow \,\,\,\left\langle {{\text{YES}}} \right\rangle \hfill \\ \,{\text{Take}}\,\,b = 4\,\,\,\, \Rightarrow \,\,\,\left\langle {{\text{NO}}} \right\rangle \hfill \\ \end{gathered} \right.$$

This solution follows the notations and rationale taught in the GMATH method.
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Re: Is the integer b divisible by 3 ? &nbs [#permalink] 04 Sep 2018, 11:44
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