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x is a positive, odd integer.

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Intern
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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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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, \(-(3^x) > -(4^x)\)

Answer: A

Cheers,
Brent
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Re: x is a positive, odd integer. [#permalink] New post 04 May 2020, 03:00
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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Re: x is a positive, odd integer. [#permalink] New post 04 May 2020, 03:48
boxing506 wrote:
pls explain the answer

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
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Re: x is a positive, odd integer. [#permalink] New post 04 May 2020, 12:02
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Nikhil4GRE wrote:
boxing506 wrote:
pls explain the answer

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)


Answer A
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Re: x is a positive, odd integer.   [#permalink] 04 May 2020, 12:02
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