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x is a positive, odd integer.

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Re: x is a positive, odd integer. [#permalink] New post 09 Jul 2018, 17:15
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So the way I approached this was by doing a guess and check method.

The values for 'x' used: 1, 2, -1. -2

x = 1 --> (-3)^1 = -3 & -2^2(1) = -4 ---> -3 > -4
x = 2 --> (-3)^2 = 9 & -2^2(2) = -16 ---> 9 > -16
x = -1 --> (-3)^(-1) = -1/3 & -2^2(-1) = -1/4 ---> -1/3 > -1/4
x = -2 --> (-3)^(-2) = 1/9 & -2^2(-2) = -1/16 ---> 1/9 > -1/16

Based on the calculations we completed, it is absolutly clear that the answer is A.
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Re: x is a positive, odd integer. [#permalink] New post 15 Aug 2018, 20:15
There is a major flaw in the Question and its solution, because my education tells me and so does mathsfirst.massey.ac.nz/Algebra/OrderOfOp/orderAlg.htm look at the last example of Implied Brackets, one must solve the Power, if it is an expression, before he/she raise the number to that power.

I think this is an erroneous use of PEMDAS here.
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Re: x is a positive, odd integer. [#permalink] New post 05 Mar 2019, 22:02
Let's not break down and follow a simplification .
B = -2^2x
now , suppose x=3
B= -2^6, which will always be positive. Answer should be B
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Re: x is a positive, odd integer. [#permalink] New post 06 Mar 2019, 09:34
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Expert's post
Carcass wrote:


x is a positive, odd integer.

Quantity A
Quantity B
\((-3)^x\)
\(-2^{2x}\)


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.


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

We're told that x is a positive, ODD integer
So, \((-3)^x = (-3)^{ODD} = (NEGATIVE)^{ODD} = NEGATIVE\)

Conversely, if x in a integer, we know that 2x is EVEN
So, \(-2^{2x} = -2^{EVEN} = (NEGATIVE)^{EVEN} = POSITIVE\)


We get:
QUANTITY A: Some NEGATIVE number
QUANTITY B: Some POSITIVE number

Answer: B

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com
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Re: x is a positive, odd integer.   [#permalink] 06 Mar 2019, 09:34
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