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x is a positive, odd integer.

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x is a positive, odd integer. [#permalink]  09 Aug 2017, 15:43
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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.
[Reveal] Spoiler: OA

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Re: x is a positive, odd integer. [#permalink]  21 Aug 2017, 06:31
pls explain the answer
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Re: x is a positive, odd integer. [#permalink]  21 Aug 2017, 10:53
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-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.

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Re: x is a positive, odd integer. [#permalink]  12 Sep 2017, 00:37
Shouldn't the answer be B?

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
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Re: x is a positive, odd integer. [#permalink]  12 Sep 2017, 02:03
Expert's post
Please refer to my explanation above.

B is -64 for instance and A is -27

On the number line (negative side) -64 is farthest from zero than -27.

Quantity B is NOT 4^x but - 4^x

Therefore, A is the answer. A is always > B

Hope this helps
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Re: x is a positive, odd integer. [#permalink]  12 Sep 2017, 03:07
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]  12 Sep 2017, 04:11
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Sorry but in this scenario, the rules for powers teach us that what you said leads to the wrong solution.

You must before multiple -2*2 = -4 the rise -4^x.

Hope this helps

regards
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Re: x is a positive, odd integer. [#permalink]  12 Sep 2017, 06:54
(-2)^x is not the same as -2^x.
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Re: x is a positive, odd integer. [#permalink]  12 Sep 2017, 11:49
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Official Explanation

[quote] 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] 12 Sep 2017, 11:49
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