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12 May 2022, 01:30
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
55% (01:26) correct
45%
(01:29)
wrong
based on 143
sessions
History
Date
Time
Result
Not Attempted Yet
Is x^2 < x^3?
(1) x < x^2
(2) x < 1
(1) x < x^2
(2) x < 1
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(1)Only
We know
x < x^2
Now, we try to multiple x at either side
if x > 0, x^2 < x^3
If x < 0, x^2 > x^3
Not sufficient
(2)Only
If x=0, x^2 = x^3
If x=-1, x^2 > x^3
Not sufficient
(1)(2)Together
We know
x < x^2 AND x < 1
if 1 > x > 0, x^2 < x^3
If x < 0, x^2 > x^3
Not sufficient
The answer is thus (E).
= = = = = = C o r r e c t i o n = = = = = =
I was wrong to write:
if 1 > x > 0, x^2 < x^3
Actually,
1 > x > 0
=> x > x^2 > 0
=> x^2 > x^3 > 0
Then
If x = 0, x^2 = x^3
If x < 0, x^2 > x^3
So we can answer "No" to the posed question.
The answer should be (B).
We know
x < x^2
Now, we try to multiple x at either side
if x > 0, x^2 < x^3
If x < 0, x^2 > x^3
Not sufficient
(2)Only
If x=0, x^2 = x^3
If x=-1, x^2 > x^3
Not sufficient
(1)(2)Together
We know
x < x^2 AND x < 1
if 1 > x > 0, x^2 < x^3
If x < 0, x^2 > x^3
Not sufficient
The answer is thus (E).
= = = = = = C o r r e c t i o n = = = = = =
I was wrong to write:
if 1 > x > 0, x^2 < x^3
Actually,
1 > x > 0
=> x > x^2 > 0
=> x^2 > x^3 > 0
Then
If x = 0, x^2 = x^3
If x < 0, x^2 > x^3
So we can answer "No" to the posed question.
The answer should be (B).
12 May 2022, 19:33
Kudos
Bookmarks
Is \(x^{2}\) < \(x^{3}\) -------- (1)
or
Is x > 1? (Divide both sides of (1) by \(x^{2}\))
(1)
Given: x < \(x^{2}\)
=> 1/x < 1
x =
{-inf, \(0^{-}\)}
U
{\(1^{+}\), +inf}
i.e x can range from -infinity to sth less than 0 and sth greater than 1 to +infinity
Therefore, cannot decide whether x > 1
(2)
Given: x < 1
Sufficient to answer "Is x >1 "
Hence B
or
Is x > 1? (Divide both sides of (1) by \(x^{2}\))
(1)
Given: x < \(x^{2}\)
=> 1/x < 1
x =
{-inf, \(0^{-}\)}
U
{\(1^{+}\), +inf}
i.e x can range from -infinity to sth less than 0 and sth greater than 1 to +infinity
Therefore, cannot decide whether x > 1
(2)
Given: x < 1
Sufficient to answer "Is x >1 "
Hence B
