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13 Dec 2022, 09:00
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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:
45%
(medium)
Question Stats:
55% (01:27) correct
45%
(01:58)
wrong
based on 40
sessions
History
Date
Time
Result
Not Attempted Yet
Is \(m < m^2 < m^3\), for all real values of m?
(1) \(m < m^3\)
(2) \(m^3 > m^2\)
(1) \(m < m^3\)
(2) \(m^3 > m^2\)
13 Dec 2022, 09:09
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I believe the answer is B:
1) If M is -1/2, then M^3 is -1/8, but m^2 is bigger than both. So answer to target Q is no. But if M is 2, then the answer to target Q is yes. INS.
2) M must be positive integer. If we try the case of negative fractions or negative integer, the inequality does not hold. If we try positive fraction, the equation does not hold. Therefore, M must be a positive integer which tells us yes to target Q.
1) If M is -1/2, then M^3 is -1/8, but m^2 is bigger than both. So answer to target Q is no. But if M is 2, then the answer to target Q is yes. INS.
2) M must be positive integer. If we try the case of negative fractions or negative integer, the inequality does not hold. If we try positive fraction, the equation does not hold. Therefore, M must be a positive integer which tells us yes to target Q.
13 Dec 2022, 14:07
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Bunuel
There are four sections of a number line that one needs to consider when solving questions related to inequality -
------------------- -1 ------------------- 0 ------------------- 1 -------------------
\(m < m^2 < m^3\) is valid when m > 1, so the question essential translates
Is m > 1
Statement 1
\(m < m^3\)
\(m^3 > m\), when m > 1 and when -1 < m < 0
Hence we do not have a definite answer to the question Is m > 1
Statement 2
\(m^3 > m^2\)
As \(m^3\) is greater than \(m^2\), we can be sure that m is not less than or equal to 0.
Between the two regions, \(m^3 > m^2\) when m > 1
Hence we have a definite answer to the question Is m > 1- Yes !
Option B
