Vincen wrote:Is |x| < 5?
(1) x^2 < 16
(2) x(x - 5) < 0
The OA is D.
Clearly Statement (1) is sufficient. But, why statement (2) is sufficient?
Let's look at x(x - 5) < 0.
To make x(x - 5) < 0, you must not assume that x is negative, else x as well as (x - 5) would be negative, making x(x - 5) positive.
So, x cannot be negative.
x cannot be either 0 or 5, else x(x - 5) would be 0.
x cannot be greater than 5. For example, say x = 6.
Then, x(x - 5) < 0 => 6*(6 - 5) < 0 => 1 not less than 0.
Thus, 0 < x < 5. Thus, |x| < 5. Sufficient.
The correct answer:
D
Hope this helps!
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-Jay
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