Is the integer k divisible by 4? (data sufficiency)

[medyaker]

Is the integer k divisible by 4?

(1) 8k is divisible by 16.
(2) 9k is divisible by 12.

I do not have a way to solve this definitively.

Thanks :)

[Guest]

Is the integer k divisible by 4?

(1) 8k is divisible by 16.
(2) 9k is divisible by 12.

I do not have a way to solve this definitively.

Thanks :)

Statement1: k could be 2 or 4... INSUFFICIENT
Statement2:k is a multiple of 4 in order to be divisible by 4...SUFFICIENT

The correct answer is B

[RonPurewal]

best way to go, if you don't get the theory right away: start running through an exhaustive list of possibilities for each statement, and see if either
(a) you can prove the statement is insufficient (in which case you're done), or
(b) a pattern emerges that will allow you to conclude that the statement is sufficient.

statement (1): just consider an exhaustive list of multiples of 16
if 8k = 16, then k = 2 --> NO
if 8k = 32, then k = 4 --> YES
insufficient

statement (2): just consider an exhaustive list of multiples of 12
if 9k = 12, then k isn't an integer
if 9k = 24, then k isn't an integer
if 9k = 36, then k = 4 --> YES
if 9k = 48, then k isn't an integer
if 9k = 60, then k isn't an integer
if 9k = 72, then k = 8 --> YES
a pattern has emerged (continue a couple more rounds if you like)
sufficient

[RonPurewal]

if you want the theory for statement (2), here it is:

* the prime factorization of 9k is 3 x 3 x (whatever goes into k)
* this factorization must contain 4, which is two 2's
* both of the 2's must be part of k, because the rest of the factorization is 3's
* therefore, k is divisible by 4

[aliag916]

Hello, I did it this way, please correct me if I am wrong, thanks!

Q stem: Is K divisible by 4?
1) 8k is divisible by 16 implies
8k/16 = integer or k/2 = integer so K is definitely divisible by 2, but we cant say for sure if its divisible by 4 or not because in some cases it is divisible and in some cases it is not. For eg k could be 2, 4, 6, 8 etc . Not Sufficient

2) 9k is divisible by 12 implies
9k/12 = integer
3k/4 = integer
so since 3 is not divisible by 4, k must be div by 4 and the ans is b.

Thank you!

[RonPurewal]

Hello, I did it this way, please correct me if I am wrong, thanks!

Q stem: Is K divisible by 4?
1) 8k is divisible by 16 implies
8k/16 = integer or k/2 = integer so K is definitely divisible by 2, but we cant say for sure if its divisible by 4 or not because in some cases it is divisible and in some cases it is not. For eg k could be 2, 4, 6, 8 etc . Not Sufficient

2) 9k is divisible by 12 implies
9k/12 = integer
3k/4 = integer
so since 3 is not divisible by 4, k must be div by 4 and the ans is b.

Thank you!

Looks good to me.

[aliag916]

Thanks u!

I want to be able to use the method above as well but am unable to understand it properly. I was not sure why you would write 8k is divisible by 16 as 8k=16 and then 8k=32 etc. What I understand is: Since 8k is divisible by 16, 8k is a multiple of 16 and so we can write it as u did.
But doesn't 8k=32 imply that 8k is divisible by 32 whereas stmt 1 states that 8k is divisible by 16? So am a little confused.

Thank you!

Ok i believe I understand, its coz of the variable integer K that can take on values.

[RonPurewal]

Thanks u!

I want to be able to use the method above as well but am unable to understand it properly. I was not sure why you would write 8k is divisible by 16 as 8k=16 and then 8k=32 etc. What I understand is: Since 8k is divisible by 16, 8k is a multiple of 16 and so we can write it as u did.

8k is any multiple of 16. So 8k could be 16, 32, 48, 64, 80, etc.
There's no need to test anything after 32, though, since the first two cases already prove the statement insufficient.

But doesn't 8k=32 imply that 8k is divisible by 32 whereas stmt 1 states that 8k is divisible by 16? So am a little confused.

32 is divisible by 16.