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Is the integer 2b divisible by 6 ? (1) 8b is divisible by

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by ceilidh.erickson » Fri Apr 08, 2016 9:09 am
First, rephrase the question:

Is the integer 2b divisible by 6 ?

--> we can turn this into: is (2b)/6 = some integer?
Then, divide numerator and denominator by 2: is b/3 = some integer?

Target question: Is b divisible by 3?

(1) 8b is divisible by 3.

We could rephrase as (8b)/3 = some integer
Since 8 is not divisible by 3, then b itself must be divisible by 3. This answers our target question.
Sufficient

(2) 9b is divisible by 12.

We can rephrase: (9b)/12 = some integer
Simplify: (3b)/4 = some integer

This tells us that b must be divisible by 4 (since 3 is not), but it does not answer the target question about whether b is divisible by 3.
Insufficient.

The answer is A.
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by [email protected] » Fri Apr 08, 2016 9:39 am
Hi eitijan,

This question can be solved in a number of different ways, including prime factorization:

We're told that 2B is an INTEGER. We're asked if 2B is divisible by 6. This is a YES/NO question.

To be divisible by 6, a number must have at least one "2" and at least one "3" when you prime factor it. For example:

18 IS divisible by 6 because 18 = (2)(3)(3)
20 is NOT divisible by 6 because 20 = (2)(2)(5)... it's missing the "3" that we need.

So this question is ultimately asking if 2B has a "2" and a "3" when you prime factor it. Since we're dealing with "2B" we know that the "2" is automatically going to be there, so we're really just looking for proof at at least one "3" is in the "B"...

1) 8B is divisible by 3

8B = (2)(2)(2)(B)

Since we're told that 8B is divisible by 3, at least one "3" is in the "B"
The answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT

2) 9B is divisible by 12

9B = (3)(3)(B)

12 = (2)(2)(3)

Here, the value of the 'B' can vary...
IF...
B = 4, then the answer to the question is NO.
B = 12, then the answer to the question is YES.
Fact 2 is INSUFFICIENT

Final Answer: A

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by mcguy » Thu Apr 14, 2016 11:55 pm
What if B is a fraction? it's not stated that B is an integer right.

If we analyze statement A : 8B div by 3 ---> B can be 3/8 for example. Hence, 2B = 6/8 and this si not divisible by 6. So A is NOT SUFFICIENT.

B alone neither is not sufficient. but A and B together are sufficient.

Right? Thanks for commenting on my reasoning.
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by GMATGuruNY » Fri Apr 15, 2016 1:24 am
mcguy wrote:What if B is a fraction? it's not stated that B is an integer right.

If we analyze statement A : 8B div by 3 ---> B can be 3/8 for example. Hence, 2B = 6/8 and this si not divisible by 6. So A is NOT SUFFICIENT.
.
Question stem:
Is the integer 2b divisible by 6?
The phrase in red implies that 2b must be an INTEGER.
In Statement 1, b=3/8 is not a valid case, since 2b = (2)(3/8) = 3/4, which is not an integer.
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by [email protected] » Fri Apr 15, 2016 8:57 am
Hi mcguy,

When TESTing VALUES in a DS question, you have to make sure that you're limiting your values to ones that 'fit' with the given information in the prompt. Here, we're told that 2B is an INTEGER. That information is rather restrictive. While B itself doesn't necessarily have to be an integer, it can't be just "any" fraction.

B COULD equal 0, 1/2, 1, 3/2, 2, 5/2, 3, 7/2, 4, etc.

When you combine this limitation with the ones included in each of the two Facts, the options become even more limited.

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by Matt@VeritasPrep » Fri Apr 15, 2016 1:32 pm
mcguy wrote:What if B is a fraction? it's not stated that B is an integer right.

If we analyze statement A : 8B div by 3 ---> B can be 3/8 for example. Hence, 2B = 6/8 and this si not divisible by 6. So A is NOT SUFFICIENT.

B alone neither is not sufficient. but A and B together are sufficient.

Right? Thanks for commenting on my reasoning.
Once you're told that 2b is an integer, you know that either b is an integer or b is x/2, where x is an integer. So b = 3/8 wouldn't work, but b = 1/2 would be fine.
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by rahulprasad11 » Mon Jul 18, 2016 10:02 am
[email protected] wrote:Hi eitijan,

This question can be solved in a number of different ways, including prime factorization:

We're told that 2B is an INTEGER. We're asked if 2B is divisible by 6. This is a YES/NO question.

To be divisible by 6, a number must have at least one "2" and at least one "3" when you prime factor it. For example:

18 IS divisible by 6 because 18 = (2)(3)(3)
20 is NOT divisible by 6 because 20 = (2)(2)(5)... it's missing the "3" that we need.

So this question is ultimately asking if 2B has a "2" and a "3" when you prime factor it. Since we're dealing with "2B" we know that the "2" is automatically going to be there, so we're really just looking for proof at at least one "3" is in the "B"...

1) 8B is divisible by 3

8B = (2)(2)(2)(B)

Since we're told that 8B is divisible by 3, at least one "3" is in the "B"
The answer to the question is ALWAYS YES.
Fact 1 is SUFFICIENT

2) 9B is divisible by 12

9B = (3)(3)(B)

12 = (2)(2)(3)

Here, the value of the 'B' can vary...
IF...
B = 4, then the answer to the question is NO.
B = 12, then the answer to the question is YES.
Fact 2 is INSUFFICIENT

Final Answer: A

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Hi Rich, I think the ans is C.
given 2b = 0,1,2,3,4,5,6,7,8,9....
or, b = 0,1/2,..,3/2,..,6/2,...,9/2

a)
if b = 3/2
then 8b = 12 i.e. 8b is divisible by 3.
but 2b = 3 -> not divisible by 6.

if b = 6/2
then 8b = 24 i.e. 8b is divisible by 3.
but 2b = 6 -> divisible by 6.

if b = 9/2
then 8b = 36 i.e. 8b is divisible by 3.
but 2b = 9 -> not divisible by 6.
Therefore, A is not sufficient.

Answer is C, which only confirms 2b's divisibility by 6.
Last edited by rahulprasad11 on Mon Jul 18, 2016 10:26 am, edited 2 times in total.
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by rahulprasad11 » Mon Jul 18, 2016 10:05 am
ceilidh.erickson wrote:First, rephrase the question:

Is the integer 2b divisible by 6 ?

--> we can turn this into: is (2b)/6 = some integer?
Then, divide numerator and denominator by 2: is b/3 = some integer?

Target question: Is b divisible by 3?

(1) 8b is divisible by 3.

We could rephrase as (8b)/3 = some integer
Since 8 is not divisible by 3, then b itself must be divisible by 3. This answers our target question.
Sufficient

(2) 9b is divisible by 12.

We can rephrase: (9b)/12 = some integer
Simplify: (3b)/4 = some integer

This tells us that b must be divisible by 4 (since 3 is not), but it does not answer the target question about whether b is divisible by 3.
Insufficient.

The answer is A.
Hi, isn't the ans C?
given 2b = 0,1,2,3,4,5,6,7,8,9....
or, b = 0,1/2,..,3/2,..,6/2,...,9/2

a)
if b = 3/2
then 8b = 12 i.e. 8b is divisible by 3.
but 2b = 3 -> not divisible by 6.

if b = 6/2
then 8b = 24 i.e. 8b is divisible by 3.
but 2b = 6 -> divisible by 6.

if b = 9/2
then 8b = 36 i.e. 8b is divisible by 3.
but 2b = 9 -> not divisible by 6.
Therefore, A is not sufficient.

Answer is C, which only confirms 2b's divisibility by 6.
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by GMATGuruNY » Mon Jul 18, 2016 11:33 am
eitijan wrote:Is the integer 2b divisible by 6 ?

(1) 8b is divisible by 3.

(2) 9b is divisible by 12.
Statement 1:
8b = 3, 6, 9, 12, 15, 18, 21, 24...

If we divide both sides by 8, we get:
b = 3/8, 3/4, 9/8, 3/2, 15/8, 9/4, 21/8, 3...
2b = 3/4, 3/2, 9/4, 3, 15/4, 9/2, 21/4, 6...

Of the resulting options for 2b, only the values in blue are integers.
The implication is that 2b must be a MULTIPLE OF 3:
3, 6, 9, 12...

If 2b = 3, then 2b is NOT divisible by 6.
If 2b = 6, then 2b IS divisible by 6.
INSUFFICIENT.

Statement 2:
9b = 12, 24, 36, 48, 60, 72...

If we divide both sides by 9, we get:
b = 4/3, 8/3, 4, 16/3, 20/3, 8
2b = 8/3, 16/3, 8, 32/3, 40/3, 16...

Of the resulting options for 2b, only the values in red are integers.
The implication is that 2b must be a MULTIPLE OF 8:
8, 16, 24, 32...

If 2b = 8, then 2b is NOT divisible by 6.
If 2b = 24, then 2b IS divisible by 6.
INSUFFICIENT.

Statements combined:
Since 2b must be a multiple of both 3 and 8, 2b must be a multiple of 24:
24, 48, 72, 96...
Thus, 2b must be divisible by 6.
SUFFICIENT.

The correct answer is C.
Last edited by GMATGuruNY on Mon Jul 18, 2016 2:33 pm, edited 1 time in total.
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by ceilidh.erickson » Mon Jul 18, 2016 11:47 am
rahulprasad11 wrote:
ceilidh.erickson wrote:First, rephrase the question:

Is the integer 2b divisible by 6 ?

--> we can turn this into: is (2b)/6 = some integer?
Then, divide numerator and denominator by 2: is b/3 = some integer?

Target question: Is b divisible by 3?

(1) 8b is divisible by 3.

We could rephrase as (8b)/3 = some integer
Since 8 is not divisible by 3, then b itself must be divisible by 3. This answers our target question.
Sufficient

(2) 9b is divisible by 12.

We can rephrase: (9b)/12 = some integer
Simplify: (3b)/4 = some integer

This tells us that b must be divisible by 4 (since 3 is not), but it does not answer the target question about whether b is divisible by 3.
Insufficient.

The answer is A.
Hi, isn't the ans C?
given 2b = 0,1,2,3,4,5,6,7,8,9....
or, b = 0,1/2,..,3/2,..,6/2,...,9/2

a)
if b = 3/2
then 8b = 12 i.e. 8b is divisible by 3.
but 2b = 3 -> not divisible by 6.

if b = 6/2
then 8b = 24 i.e. 8b is divisible by 3.
but 2b = 6 -> divisible by 6.

if b = 9/2
then 8b = 36 i.e. 8b is divisible by 3.
but 2b = 9 -> not divisible by 6.
Therefore, A is not sufficient.

Answer is C, which only confirms 2b's divisibility by 6.
I made a classic GMAT mistake! I read "the integer 2b" and assumed that b itself was an integer! You're right - good eye.

I'm not going to edit my post, because it's helpful for others to see that a) this is a common mistake to fall for, and b) even experts make mistakes! :) You can still get a top score if you make mistakes, as long as you learn from them.
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Harvard Graduate School of Education
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