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18 May 2022, 02:30
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86% (00:39) correct
14%
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m is negative, and n is an integer. Is m^n positive?
(1) m is odd.
(2) n is odd.
(1) m is odd.
(2) n is odd.
19 May 2022, 18:30
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If m is negative, then to make it positive we need even power to make the total positive.
The concept is that we simply need to know whether the exponent is even or odd to give the answer
Answer is B
The concept is that we simply need to know whether the exponent is even or odd to give the answer
Answer is B
20 May 2022, 07:43
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Bunuel
m is negative, and n is an integer. Is m^n positive?
(1) m is odd.
(2) n is odd.
Given: m is negative, and n is an integer.(1) m is odd.
(2) n is odd.
Target question: Is m^n positive?
-----------------ASIDE--------------------------------------------------
Two important rules:
ODD exponents preserve the sign of the base.
So, (NEGATIVE)^(ODD integer) = NEGATIVE
and (POSITIVE)^(ODD integer) = POSITIVE
An EVEN exponent always yields a positive result (unless the base = 0)
So, (NEGATIVE)^(EVEN integer) = POSITIVE
and (POSITIVE)^(EVEN integer) = POSITIVE
--------------------------------------------------------------------------
Since we're told m is NEGATIVE, we know that, if n is ODD, then m^n will be NEGATIVE, and if n is EVEN, then m^n will be POSITIVE
Statement 1: m is odd.
Since we don't have any information about whether n is ODD or EVEN, statement 1 is NOT SUFFICIENT.
For example, if m = -1 and n = 1, then m^n is negative
Conversely, , if m = -1 and n = 2, then m^n is positive
Statement 2: n is odd
So, m^n = NEGATIVE^ODD = negative
The answer to the target question is m^n is definitely NOT positive
Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Answer: B
