E.

check when \(\frac{1}{(x+1)}\) = \(\frac{x}{2}\)
x=1 and x = -2

(1) not sufficient x=1 is within the range
(2) not sufficient both x=1 and x=-2 are within the range

(1) + (2) not sufficient, x=1 is still within the range, which is <0,3)

Is \(\frac{1}{x + 1} > \frac{x}{2}\), is a Yes/No type of question, where plugging in of values helps.


Constraints: x \(\neq\) -1, which means x can be an integer or fraction other than -1.



Statement 1: \(x \geq 0\)

Putting x = 0, we get \(\frac{1}{x + 1} = \frac{1}{0 + 1} = 1\) and \(\frac{x}{2} = \frac{0}{2} = 0\).

Therefore \(\frac{1}{x + 1} \space is \space > \frac{x}{2}\)


Putting x = 1, we get \(\frac{1}{x + 1} = \frac{1}{1 + 1} = \frac{1}{2}\) and \(\frac{x}{2} = \frac{1}{2}\).

Therefore \(\frac{1}{x + 1} \space is \space = \frac{x}{2}\)



Therefore Statement 1 Alone is Insufficient. Answer options could be B, C or E



Statement 2: x < 3.



Again if we put x = 0 and x = 1 (Since both are < 3), we will get the same answer as in Statement 1.


Therefore Statement 2 Alone is Insufficient. Answer options could be C or E



Combining Both Statements: [/u][/i]. \(x \geq 0\) and x < 3.


Again x = 0 and x = 1 lie within the range of values that satisfy the above conditions, and we still get 2 different relationships as seen before.


Therefore Both statements combined are Insufficient.



Option E

Arun Kumar
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