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06 Sep 2023, 08:00
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
62% (01:45) correct
38%
(01:25)
wrong
based on 39
sessions
History
Date
Time
Result
Not Attempted Yet
06 Sep 2023, 09:35
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Is \(x^2-x>0\)?
Means that
x(x-1) > 0
So, either both i.e. x and x-1 are positive or both are negative.
A. When both are positive
x > 0 and x - 1 > 0
Thus,
x > 1
is always true.
B. When both are negative
x < 0 and x -1 < 0
Thus,
x < 0
is always true.
Either x > 1 or x < 0
(1) \(x>0\)
x = 1/2, NO
x = 2, YES
INSUFFICIENT.
(2) \(x^3+x>0\)
x(x^2 + 1) > 0
So, both are positive(both can't be negative since x^2 + 1 is always positive)
When both are positive
x > 0 and x^2 + 1 > 0
Here x /= 0
Thus,
x > 0
is always true.
Which gives both YES and NO with x = 1 and x = 1/2 respectively.
INSUFFICIENT.
Together 1 and 2
x > 0
Above cases discussed leads us to INSUFFICIENCY.
Answer E.
Means that
x(x-1) > 0
So, either both i.e. x and x-1 are positive or both are negative.
A. When both are positive
x > 0 and x - 1 > 0
Thus,
x > 1
is always true.
B. When both are negative
x < 0 and x -1 < 0
Thus,
x < 0
is always true.
Either x > 1 or x < 0
(1) \(x>0\)
x = 1/2, NO
x = 2, YES
INSUFFICIENT.
(2) \(x^3+x>0\)
x(x^2 + 1) > 0
So, both are positive(both can't be negative since x^2 + 1 is always positive)
When both are positive
x > 0 and x^2 + 1 > 0
Here x /= 0
Thus,
x > 0
is always true.
Which gives both YES and NO with x = 1 and x = 1/2 respectively.
INSUFFICIENT.
Together 1 and 2
x > 0
Above cases discussed leads us to INSUFFICIENCY.
Answer E.
06 Sep 2023, 10:32
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Asked: Is x(x-1)>0 or we can convert the question stem to "Is x<0 or x>1"?
Statement 1: x>0
We don't know how big is x. If x is 0.5, we get No.
If x is 3, we get Yes. NS.
Statement 2: x(x\(^2\) + 1)>0
we know the term (x\(^2\) + 1) will always be positive. So we get x>0, which is similar to statement 1 and we can't deduce anything from this. NS
On combining too, we get no new information.
Answer: E.
Statement 1: x>0
We don't know how big is x. If x is 0.5, we get No.
If x is 3, we get Yes. NS.
Statement 2: x(x\(^2\) + 1)>0
we know the term (x\(^2\) + 1) will always be positive. So we get x>0, which is similar to statement 1 and we can't deduce anything from this. NS
On combining too, we get no new information.
Answer: E.
