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22 Jan 2023, 02:20
Kudos
Bookmarks
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:
50% (02:02) correct
50%
(02:34)
wrong
based on 20
sessions
History
Date
Time
Result
Not Attempted Yet
Is \(k + \frac{1}{k} < -1\) ?
(1) \(k^2 < 1\)
(2) \(k^3 + k^2 + k < 0\)
(1) \(k^2 < 1\)
(2) \(k^3 + k^2 + k < 0\)
22 Jan 2023, 23:17
Kudos
Bookmarks
Bunuel
\(k + \frac{1}{k} < -1\)
\(\frac{k^2 + 1 +k}{k }< 0\)
Multiplying by \(k^2\) on both sides
\(k(k^2+k+1) < 0\)
Let's start with Statement 2
Statement 2
\(k^3 + k^2 + k < 0\)
\(k(k^2 + k + 1) < 0\)
This is same as what's asked. Hence this statement is sufficient.
Eliminate A , C and E.
Statement 1
\(k^2 < 1\)
-1 < k < 1
Case 1: k = 0.5
\(k + \frac{1}{k} > 0\)
Hence Is \(k + \frac{1}{k} < -1\), the answer is No !
Case 1: k = -0.5
\(k + \frac{1}{k} = -0.5 + \frac{1}{-0.5} = -2.5\)
Is \(k + \frac{1}{k} < -1\), the answer is Yes !
The statement is not sufficient
Option B
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