srisl11 wrote:2x-1 is odd => 2x is even
2x will be even only if x is an integer
2(1.5) = 3 (odd)
2(4.5) = 9 (odd)

So x must be an integer for 2x to be even

tritrantran wrote:

srisl11 wrote:2x-1 is odd => 2x is even
2x will be even only if x is an integer
2(1.5) = 3 (odd)
2(4.5) = 9 (odd)

So x must be an integer for 2x to be even

Can X be even and not be an integer?

2(1.6) = 3.2 (even)

anayeri wrote:What's the general rule of thumb on assumptions Stuart?

I feel like on most cases - there's some degree of assuming. Are there certain things that we should be looking out for? (ie integers would be a good example: "never assume an integer unless otherwise stated")?

Any other ones that are common assumption errors?

naveedakhan wrote:2x can either be even or odd, doesn't matter, according the statement 1, we only take the values of x for which the compete statement (2x-1) is odd.
The only reason of ruling out A would be if x=0 because 2(0)-1=-1 which is odd but that x=0 is even, otherwise for any other values, either fractions or negatives, as long as 2x-1 churns out an odd number, the value for x can be taken as such.

Stuart...please comment

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).