Question does require some clarification for me.
Lets just focus on B
k is not divisible by any odd integer greater than 1
I can be sure of only one thing here, that is K is even, or it can be raised to the power of 2.
What is the definite value of K cannot be obtained by statement 2, under any circumstances, I think all of us agree.
e.g, K could be 2, 4, 8,16,32 etc
Now question is
Is k equal to 2^r for some positive integer r?
If K=2 and r=2,then is 2 = 2^2 answer is No 2 \neq 4 { there is no restriction on the value of k other than it has no odd factors greater than 1 and r has no restriction other than it is an integer, so k=2 and r=2 are both valid}
If K=4 and r=3,then is 4 = 2^3 answer is No 4 \neq 8 { there is no restriction on the value of k other than it has no odd factors greater than 1 and r has no restriction other than it is an integer, so k=4 and r=3 are both valid}
If K=4 and r=2,then is 4 = 2^2 Answer is Yes 4 = 4 { there is no restriction on the value of k other than it has no odd factors greater than 1 and r has no restriction other than it is an integer, so k =4 and r=2 are both valid}
So we can see depending upon r ,2^rchanges .
so we can get both a Yes and a No depending upon K and r, can we not?
We do not have a definite K and a definite r, from 2
If question could have stated does K have only 2 as prime factors then of course solution could be more justified. I think some of us do agree that solution is debatable.
Please do correct, if there is anything wrong with the reasoning above, not entirely confident in challenging solution of GMAT prep.
Lets just focus on B
k is not divisible by any odd integer greater than 1
I can be sure of only one thing here, that is K is even, or it can be raised to the power of 2.
What is the definite value of K cannot be obtained by statement 2, under any circumstances, I think all of us agree.
e.g, K could be 2, 4, 8,16,32 etc
Now question is
Is k equal to 2^r for some positive integer r?
If K=2 and r=2,then is 2 = 2^2 answer is No 2 \neq 4 { there is no restriction on the value of k other than it has no odd factors greater than 1 and r has no restriction other than it is an integer, so k=2 and r=2 are both valid}
If K=4 and r=3,then is 4 = 2^3 answer is No 4 \neq 8 { there is no restriction on the value of k other than it has no odd factors greater than 1 and r has no restriction other than it is an integer, so k=4 and r=3 are both valid}
If K=4 and r=2,then is 4 = 2^2 Answer is Yes 4 = 4 { there is no restriction on the value of k other than it has no odd factors greater than 1 and r has no restriction other than it is an integer, so k =4 and r=2 are both valid}
So we can see depending upon r ,2^rchanges .
so we can get both a Yes and a No depending upon K and r, can we not?
We do not have a definite K and a definite r, from 2
If question could have stated does K have only 2 as prime factors then of course solution could be more justified. I think some of us do agree that solution is debatable.
Please do correct, if there is anything wrong with the reasoning above, not entirely confident in challenging solution of GMAT prep.