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TAGS: Founder  Joined: 18 Apr 2015
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x is a positive, odd integer. [#permalink]
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Expert's post 00:00

Question Stats: 30% (00:42) correct 69% (00:25) wrong based on 242 sessions Founder  Joined: 18 Apr 2015
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GRE 1: Q160 V160 Followers: 316

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Re: x is a positive, odd integer. [#permalink]
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Expert's post
-3 raised to odd integers always is negative. $$-3 ^1 =-3$$; $$-3^3 = -27$$ and so on....

$$-2^{2x}$$ becomes $$-4^x$$ and -4 raised to odd integer power is always negative: $$-4^1 = -4$$ ; $$-4^3 = -64$$

As you can see A is always greater than B.

Hope now is clear.

Regards
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Re: x is a positive, odd integer. [#permalink]
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Since x is odd and positive,
Quantity A will always be negative

Quantity B: $$(-2)^2)^x = 4^x$$
Hence quantity B will always be positive
Founder  Joined: 18 Apr 2015
Posts: 13939
GRE 1: Q160 V160 Followers: 316

Kudos [?]: 3690 , given: 12953

Re: x is a positive, odd integer. [#permalink]
Expert's post VP Joined: 20 Apr 2016
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Re: x is a positive, odd integer. [#permalink]
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Plz Clarify -

"2^{2x} becomes -4^x and -4 raised to odd integer power is always negative: -4^1 = -4 ; -4^3 = -64"

Now if I consider this way will it be wrong-

x=1

In B;

-2^{2x} = -2^{2.1} [since x=1]

=-2^{2} [2.1 = 2] = +4
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Re: x is a positive, odd integer. [#permalink]
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Expert's post
Intern Joined: 26 Aug 2017
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Re: x is a positive, odd integer. [#permalink]
(-2)^x is not the same as -2^x.
Founder  Joined: 18 Apr 2015
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Re: x is a positive, odd integer. [#permalink]
Expert's post
Official Explanation

In Quantity A, a negative integer is raised to a positive odd power. Odd powers retain the sign of the underlying quantity. Thus, (−3)x = −3x. Meanwhile, in Quantity B, the exponent may be broken up as follows, so as to match that in Quantity A: - $$2^2x$$ = ($$2^2$$)^x = $$4x$$. Note that the minus sign is applied after the multiplication, for both quantities. Both columns are negative;

A) $$-3^x$$

B) $$-4^x$$

However, for positive x, $$3^x < 4^x$$, so that

- $$3^x$$ > - $$4^x$$. Therefore Quantity A is larger.
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Re: x is a positive, odd integer. [#permalink]
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Watch this
bparth94 wrote:

Since x is odd and positive,
Quantity A will always be negative

Quantity B: $$(-2)^2)^x = 4^x$$
Hence quantity B will always be positive Manager Joined: 22 Feb 2018
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Re: x is a positive, odd integer. [#permalink]
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x is odd, thus (-3)^x is negative.
-2^2x, because 2x is even, -2 to power of an even value is positive.
So B is bigger than A
*also we can thick ofB as: (-2^2x) = ((-2)^2)^x = 4^x which is positive.

_________________ Manager Joined: 29 Nov 2017
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Re: x is a positive, odd integer. [#permalink]
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People fell in the trap of not comprehending Quantity A: - 2^2x = − (2^2)^x = − 4x.
Intern Joined: 08 Apr 2018
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Re: x is a positive, odd integer. [#permalink]
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.

If the answer to this is B, this question was not properly written. According to PEMDAS, powers get precedence and 2x will always be even (rule of even x odd = even). Hence, any negative number raised to an even positive power will always be positive.
Intern Joined: 08 Apr 2018
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Re: x is a positive, odd integer. [#permalink]
Emike56 wrote:
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.

If the answer to this is B, this question was not properly written. According to PEMDAS, powers get precedence and 2x will always be even (rule of even x odd = even). Hence, any negative number raised to an even positive power will always be positive.

Also, what I can see you people who say A is greater do is square -2 before applying the odd value of x which is never correct mathematically. Treat 2x like they are in a bracket before applying to -2 to get your answer.
Founder  Joined: 18 Apr 2015
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Re: x is a positive, odd integer. [#permalink]
Expert's post
Manager Joined: 27 Feb 2017
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Kudos [?]: 78 , given: 15

Re: x is a positive, odd integer. [#permalink]
Even after reading all these discussion, I do not understand this.

If x=1, A = -3 and B= +4. How is the answer A then? I think the answer should be D
Founder  Joined: 18 Apr 2015
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Kudos [?]: 3690 , given: 12953

Re: x is a positive, odd integer. [#permalink]
Expert's post
Manager Joined: 22 Feb 2018
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Re: x is a positive, odd integer. [#permalink]
A: x is odd, thus -3 in power of something odd is negative.
B: x is odd, but it is not important because power of -2 is 2x which is always even. So B is a positive value.

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Re: x is a positive, odd integer. [#permalink]
I think the question is really misleading but do such questions appear on the test? I do not understand why are we taking -2^2x as -4^x. It can also be thought of as (-2)^2x. In this case, B will be greater. VP Joined: 20 Apr 2016
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Re: x is a positive, odd integer. [#permalink]
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kruttikaaggarwal wrote:
I think the question is really misleading but do such questions appear on the test? I do not understand why are we taking -2^2x as -4^x. It can also be thought of as (-2)^2x. In this case, B will be greater.

There is a catch in this problem

If we look at statement 1 we have
$$(-3)^x$$

now any odd value of x it will be negative with multiples of 3.

Now for statement 2;

we have

-$$2^{2x}$$

Now the negative sign will always be present since we are not squaring the sign as it is not under bracket as in statement 1.

Therefore any odd values of x in equation 2 will always be less than the value in equation 1
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Re: x is a positive, odd integer. [#permalink]
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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. Re: x is a positive, odd integer.   [#permalink] 09 Jul 2018, 17:15
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