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01 Nov 2018, 08:35
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E
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If x ≠ −1, which is greater, \(\frac{1}{(x+1)}\) or \(\frac{x}{2}\) ?
(1) x ≥ 0
(2) x < 3
(1) x ≥ 0
(2) x < 3
02 Nov 2018, 05:19
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gmatbusters
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)
05 Sep 2020, 01:10
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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
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
