Data Sufficiency

Is x odd?

1) 2x-1 is odd
2) x^3 is odd


OA after some discussions please ...
Source :Kaplan

I am getting B)

Whats the OA?

OA is C

damn...i got B too

Interesting....


If x is even x^3 can never be odd. x has to be odd. I still feel OA should be B) and not C). If it is for sure C) then I am missing something here!

2X-1 does not help us in any way to determine if x is odd or even. x can be odd or even.

So not sure how combining this with x^3 odd does it...

Sris,
Have they given an official explanation on how its C)? I am curious to know. :roll:

I took B first...
There is explanation in Kaplan (otherwise I would have taken it for granted that there is a "print mistake" and the OA is B. )
Its a lengthy explanation for statement 1 ..I will type and post it soon

For B the explanation is
B will fail if x = cubeth root of 7
because in this case x^3 will be odd but x is not odd

Ok thanks!

Looking forward to stmt I and II combined sufficiency explanation!

I think we missed it since we considered only integers when no info was given about x. This is where these problems get us...

Looking at this... what I can think of the top of my head is if x=0 then statement 2 will fail since 0=even.

Looking at this... what I can think of the top
of my head is if x=0 then statement 2 will fail since 0=even.

Its given x^3 is odd is true so x cant be 0

Yes you are right, i rushed with my statement.

srisl11 wrote:Is x odd?

1) 2x-1 is odd
2) x^3 is odd


OA after some discussions please ...
Source :Kaplan

Never make assumptions!

To get (B), one has to assume that x is an integer. However, we're never told that's the case.

Is x odd?

(1) 2x - 1 = odd
2x = even

For 2x to be even, x could be an even or odd integer: insufficient.

(2) x^3 = odd

For x^3 to be odd, x could be an odd integer or the cube root of an odd integer: insufficient.

Together: from (1), we know that x is an integer; from (2), we know that if x is an integer, it must be odd. Therefore, we now know that x must be an odd integer: sufficient.

Together sufficient, apart insufficient: choose (C).

Explanation given in Kaplan:

Statement 1 tells you that 2x-1 is odd . That is , 2x must be even since any number that is one more than an odd number must be even. Because 2x is even ,2x is 2 multiplied by an integer N . So 2x=2N. and x=N . THis means that N must be an integer. However , since any integer multiplied by 2 is even , you cannot say whether x is odd or even . So since x can be odd or even this statement is by itself insufficient and you can discard answer choices (1) and (4)

Statement 2 tells you that x^3 is an integer , then since the product of any set of integers is odd if each of those integers id odd , x must be odd. However , x could also be an irrational number like cubeth root 7 .
In this case x^3 is odd but x is not odd ,it's not an integer at all.
So Statement 2 is insuff

Now combine St 1 and St 2 .
From st 1 we know that x is an integer, while from st 2 we know that x is odd.
The product of any set of integers is odd only if each of those integers is odd. So x must be odd and the statements taken together are sufficient.

Reading the other answers now... as Kaplan explains if x = cubeth root of 7

x^3=odd will fail (it will be odd but x won't be odd, yes it won't be even either but it's not odd)

and since we have no restrictions for x i guess this is really possible.

Stuart Kovinsky wrote:

srisl11 wrote:Is x odd?

1) 2x-1 is odd
2) x^3 is odd


OA after some discussions please ...
Source :Kaplan

Never make assumptions!

To get (B), one has to assume that x is an integer. However, we're never told that's the case.

Is x odd?

(1) 2x - 1 = odd
2x = even

For 2x to be even, x could be an even or odd integer: insufficient.

(2) x^3 = odd

For x^3 to be odd, x could be an odd integer or the cube root of an odd integer: insufficient.

Together: from (1), we know that x is an integer; from (2), we know that if x is an integer, it must be odd. Therefore, we now know that x must be an odd integer: sufficient.

Together sufficient, apart insufficient: choose (C).

THanks Stuart , Your explanation is very clear and easy to understand

Nice problem!

Takeaway for all of us : Like Stuart mentioned dont assume when no info about variables in question are given.