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

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Difficulty:   15% (low)

Question Stats: 78% (00:56) correct 22% (00:56) wrong based on 220 sessions

### HideShow timer Statistics If n is an integer, is $$-3x^n$$ positive?

(1) x is negative.
(2) n is odd.

Originally posted by ninomoi on 15 May 2007, 02:03.
Last edited by Bunuel on 08 Oct 2016, 02:57, edited 2 times in total.
Renamed the topic and edited the question.
Senior Manager  Joined: 03 May 2007
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Re: If n is an integer, is -3x^n positive?  [#permalink]

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1
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: 18
Re: If n is an integer, is -3x^n positive?  [#permalink]

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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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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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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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Re: If n is an integer, is -3x^n positive?  [#permalink]

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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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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?
Math Expert V
Joined: 02 Aug 2009
Posts: 7764
Re: If n is an integer, is -3x^n positive?  [#permalink]

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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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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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If n is an integer, is -3x^n positive?  [#permalink]

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ninomoi wrote:
If n is an integer, is $$-3x^n$$ positive?

(1) x is negative.
(2) n is odd.

Given: n = Integer

Question : $$-3x^n$$ > 0 ?

Or, Is -3 * x^n > 0 ?

Or, Is x^n > 0 ?

St 1: x < 0, but we don't know whether "n" is even or odd.

If "n" is even the answer to the question is YES

If "n" is odd the answer to the question is NO (Insufficient)

St 2: n is odd, we don't know "x" is positive or negative.

If "x" is positive the answer to the question is YES

If "x" is negative the answer to the question is NO (Insufficient)

Combining both statements we get,

x is -ve and n is odd, therefore we can say that x^n < 0 always.

Answer to the question is "NO"

Sufficient (C)
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