sanju09 wrote:
Is K a positive number?
(1) |K^3| + 1 > K.
(2) K + 1 > |K^3|.
OA E
Source: gmatclub
In the question it is not mentioned whether k is integer. So, we should not assume it to be an integer.
consider 1st option:
if k > 1, K^3 will be greater than k, so |k^3| + 1 > k.
if 0 < k < 1, k will be less than 1, so it will be less than |k^3| + 1.
if k = 1 or 0, |K^3| + 1 > K
if k < 0. k will be less than positive number (|k^3| + 1).
hence, it will satisfy for all numbers. So , we can`t answer with this option.
consider 2nd option:
k + 1 > |k^3|
if 0 < k < 1, k will be greater than |k^3|. so , the range will satisfy k + 1 > |k^3|
this will also satisfy for some negative values greater than -1. for example take -1/10 as k. it will satisfy the condition.
k + 1 = -k^3 (for exact value of k, we can solve the equation and get it. but it would be waste of our time when we are giving the exam)
so, with this condition also we got a range, which lies in both positive and negative numbers.
considering 1 and 2 together,
it will be the range matching for both the equations. Which will be the range of 2nd option taken alone. As the 1st option is true for all numbers.
hence, it is
E
