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Intern Joined: 10 Sep 2017
Posts: 2
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Kudos [?]: 3 , given: 2

Re: x is a positive, odd integer. [#permalink]
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.
Intern Joined: 21 Nov 2018
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Kudos [?]: 5 , given: 1

Re: x is a positive, odd integer. [#permalink]
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 GRE Instructor Joined: 10 Apr 2015
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Kudos [?]: 4754  , given: 70

Re: x is a positive, odd integer. [#permalink]
1
KUDOS
Expert's post
Carcass wrote:

x is a positive, odd integer.

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

The important thing to remember here is that the negative sign in front of $$-2^{2x}$$ tells us to take the value of $$2^{2x}$$ and then multiply it by $$-1$$
So, we can say that $$-2^{2x}=-(2^{2x})$$

Given:
QUANTITY A: $$(-3)^x$$
QUANTITY B: $$-(2^{2x})$$

Useful property (aka Power of a Power law): $$(b^x)^y = b^{xy}$$

Let's apply this property in reverse to rewrite Quantity B as follows:
QUANTITY A: $$(-3)^x$$
QUANTITY B: $$-[(2^2)^x]$$

Simplify Quantity B:
QUANTITY A: $$(-3)^x$$
QUANTITY B: $$-(4^x)$$

Rewrite Quantity A as follows:
QUANTITY A: $$[(-1)(3)]^x$$
QUANTITY B: $$-(4^x)$$

Apply the Power of a Product Law to get:
QUANTITY A: $$(-1)^x(3^x)$$
QUANTITY B: $$-(4^x)$$

We are told that x is an ODD integer, we know that $$(-1)^x$$ preserves its sign.
In other words, $$(-1)^x = -1$$

So we can write:
QUANTITY A: $$-(3^x)$$
QUANTITY B: $$-(4^x)$$

For every positive integer x, we know that $$3^x < 4^x$$
So, we can also conclude that, for every positive integer x, $$-(3^x) > -(4^x)$$

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com Manager Joined: 04 Apr 2020
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Kudos [?]: 42 , given: 22

Re: x is a positive, odd integer. [#permalink]
The main confusion here is because the brackets are not specified in Quantity B. I fell into this trap too.
Quantity B is supposed to be: -(2^2x) and not (-2)^2x. This makes a huge difference, because irrespective of x, this quantity is going to remain negative.

The main counter argument to those arguing that the absence of brackets introduces a lot of ambiguity is that Quantity A DOES USE BRACKETS. (-3)^x is shown explicitly. Which means if they intended Quantity B to be (-2)^2x, they would have specified the brackets.
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Kudos [?]: 5 , given: 13

Re: x is a positive, odd integer. [#permalink]
boxing506 wrote:

I think the answer is B as x is odd integar..and also i couldnot understand the power for -2 is (2X) or only X GRE Instructor Status: Entrepreneur | GMAT, GRE, CAT, SAT, ACT coach & mentor | Founder @CUBIX | Edu-consulting | Content creator
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Re: x is a positive, odd integer. [#permalink]
1
KUDOS
Nikhil4GRE wrote:
boxing506 wrote:

I think the answer is B as x is odd integar..and also i couldnot understand the power for -2 is (2X) or only X

x is a positive, odd integer.

Quantity A: (-3)^x
Quantity B: -2^(2x)

Note the difference in the 2 expressions:

Qty A: the power of x is applicable on (-3)
Qty B: the power of 2x is applicable on 2 and then the result is negated

Since x is odd: (-3) is raised to an odd power
=> [(-1)*(3)] is raised to an odd power

Thus, $$(-1)^x = -1$$ and 3^x remains as it is

Hence: Quantity A: $$-3^x$$

Also, Quantity B: -2^(2x) = -1 * 2^(2x) = -1 * (2^2)^x = -1 * 4^x = $$- 4^x$$

Thus, we now need to compare: $$- 3^x$$ and $$- 4^x$$

Clearly, $$3^x < 4^x$$ since x is positive integer

=> $$- 3^x > - 4^x$$ (inequality reverses on multiplying a negative)

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