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If n is an integer, is -3x^n positive?

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Joined: 09 Sep 2004
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If n is an integer, is -3x^n positive? [#permalink]

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15 May 2007, 01:03
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If n is an integer, is $$-3x^n$$ positive?

(1) x is negative.
(2) n is odd.
[Reveal] Spoiler: OA

Last edited by Bunuel on 08 Oct 2016, 01:57, edited 2 times in total.
Renamed the topic and edited the question.
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Re: If n is an integer, is -3x^n positive? [#permalink]

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15 May 2007, 06:52
1
KUDOS
ninomoi wrote:
If n is an integer, is -3x^n positive?

1. x is negative
2. n is odd

pls explain. Thanks

in order for the expression to be positive we have to have x negative (-*-=+)
but we also know that x^n where n is even will give us positive number
-2^2=-2*-2=4 so we have to have n odd
Intern
Joined: 29 Mar 2010
Posts: 19
Re: If n is an integer, is -3x^n positive? [#permalink]

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29 Mar 2010, 12:58
Gmat Prep says the answer is C, but I think it is A. Can someone tell me what I am doing wrong?

1. x is negative

So, let x be -1.
1 ^ 2 * - * -3 = 3
1 ^ 3 * - * -3 = 3

If x is negative the answer is always positive. If the problem were -3(x)^n then that answer would be C. However, without the brackets you must distribute the negative after you take x^n...therefore the answer will always be a negative number multiplied by -3 which gives a positive answer.
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Re: If n is an integer, is -3x^n positive? [#permalink]

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01 Apr 2010, 12:01
Gmat Prep says the answer is C, but I think it is A. Can someone

If x is negative the answer is always positive. If the problem were -3(x)^n then that answer would be C. However, without the brackets you must distribute the negative after you take x^n...therefore the answer will always be a negative number multiplied by -3 which gives a positive answer.

I think it's an issue of order of operations. Exponents come before multiplication so if x = -1 and n is even say 2
Then -3 * -1^2 = -3 * 1 = -3

x = -1 and n is odd say 3
then -3 * -1^3 = -3 * -1 = 3

so A by itself is insufficient....
Please correct me if I am wrong
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Re: If n is an integer, is -3x^n positive? [#permalink]

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01 Apr 2010, 13:00
PeterFaulkner wrote:
Gmat Prep says the answer is C, but I think it is A. Can someone

If x is negative the answer is always positive. If the problem were -3(x)^n then that answer would be C. However, without the brackets you must distribute the negative after you take x^n...therefore the answer will always be a negative number multiplied by -3 which gives a positive answer.

I think it's an issue of order of operations. Exponents come before multiplication so if x = -1 and n is even say 2
Then -3 * -1^2 = -3 * 1 = -3

x = -1 and n is odd say 3
then -3 * -1^3 = -3 * -1 = 3

so A by itself is insufficient....
Please correct me if I am wrong
But you can raise a negative number to an even power and the answer is still negative. -1^2 = -1. For it to be positive you must use brackets around the -1....(-1)^2 = 1. This is why I chose answer a. Are we to assume there are brackets on the GMAT even though they are not shown?
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If n is an integer, is -3x^n positive? [#permalink]

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11 Jan 2016, 20:14
If n is an integer, is -3x^n positive?
(1) x is negative.
(2) n is odd.

pls press kudos if you liked the question
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Posts: 5662
Re: If n is an integer, is -3x^n positive? [#permalink]

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11 Jan 2016, 20:23
NoHalfMeasures wrote:
If n is an integer, is -3x^n positive?
(1) x is negative.
(2) n is odd.

pls press kudos if you liked the question

Hi,
what does the sign of -3x^n depends on ...
1) sign of x..
2) value(odd/even) of n, and not on sign of n, as it will turn the x variable in a fraction but will not effect the sign of that fraction or integer..

lets see the statements..
(1) x is negative.
we are told of one of the two things required .. insuff

(2) n is odd.
we are told of one of the two things required .. insuff

combined both the info is provided ... suff
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Re: If n is an integer, is -3x^n positive? [#permalink]

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17 Jan 2016, 05:51
chetan2u wrote:
NoHalfMeasures wrote:
If n is an integer, is -3x^n positive?
(1) x is negative.
(2) n is odd.

pls press kudos if you liked the question

Hi,
what does the sign of -3x^n depends on ...
1) sign of x..
2) value(odd/even) of n, and not on sign of n, as it will turn the x variable in a fraction but will not effect the sign of that fraction or integer..

lets see the statements..
(1) x is negative.
we are told of one of the two things required .. insuff

(2) n is odd.
we are told of one of the two things required .. insuff

combined both the info is provided ... suff

I don't understand -- if x is negative then -3(x) = positive number and -3x^n will be positive -- is it for PEMDAS?

That x^n operation must come first?
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Joined: 02 Aug 2009
Posts: 5662
Re: If n is an integer, is -3x^n positive? [#permalink]

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17 Jan 2016, 06:02
lpetroski wrote:
chetan2u wrote:
NoHalfMeasures wrote:
If n is an integer, is -3x^n positive?
(1) x is negative.
(2) n is odd.

pls press kudos if you liked the question

Hi,
what does the sign of -3x^n depends on ...
1) sign of x..
2) value(odd/even) of n, and not on sign of n, as it will turn the x variable in a fraction but will not effect the sign of that fraction or integer..

lets see the statements..
(1) x is negative.
we are told of one of the two things required .. insuff

(2) n is odd.
we are told of one of the two things required .. insuff

combined both the info is provided ... suff

I don't understand -- if x is negative then -3(x) = positive number and -3x^n will be positive -- is it for PEMDAS?

That x^n operation must come first?

Hi,
x^n operation is not there in PEMDAS..
because x^n is one number..
example 4=2^2 so if we have 7*2^2, it means 7*4, because 2^2 is one number..
same goes for x^n..
hence even sign of n is important..
because power of an even number will make any number positive, even if it is negative..
say x=-2 and n=2..
(-2)^2=-2*-2=4, whereas -2^3=-2*-2*-2=-8, a -ive number..
hope it helps
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Re: If n is an integer, is -3x^n positive? [#permalink]

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07 Oct 2016, 21:01
ninomoi wrote:
If n is an integer, is -3x^n positive?

1. x is negative
2. n is odd

pls explain. Thanks

For the given statement to be positive x should be negative and n should be odd number
St 1 :
states that x is negative but we dont know if n is even or odd if n is even insuff if n is odd sufficient so st 1 is insuff
St 2:
States that n is odd again we dont know the value of x whether positive or negative if positive answer to question is no if negative answer to ques is yes again insuff

Combined sufficient since n is odd and x is negative statement will be positive.
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Re: If n is an integer, is -3x^n positive? [#permalink]

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24 Jan 2018, 03:46
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Re: If n is an integer, is -3x^n positive?   [#permalink] 24 Jan 2018, 03:46
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