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Is integer x positive? [#permalink]
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02 Aug 2010, 16:47
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Is integer x positive? (1) x > x^3 (2) x < x^2
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Re: 700 LEVEL QUESTION [#permalink]
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02 Aug 2010, 17:37
My attempt: Is integer X positive? 1. X > X^3 A number is greater than number raised to an odd powers implies that the number is an negative integer since a number raised to an odd power would retain its sign. Ex: 2 > (2)^3 Hence X is negative. Sufficient 2. X < X^2 A number raised to an even power would mask its sign. Hence X^2 would always be positive. Ex :1 2 < (2)^2 Ex :2 3 < 3^2 Hence X can be either positive or negative. Insufficient Answer is A is alone sufficient to solve this problem.
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Re: 700 LEVEL QUESTION [#permalink]
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03 Aug 2010, 11:53
I'd say C:
The question is: is X>0 ?
1) X > X^3
X can be negative: If X=5, 5 > 75 is true X can be positive: If X=0,3 0,3 > 0.027 is true
Hence, not sufficient
2) X < X^2
X can be negative: If X=5, 5<25 is true X can be positive: If X=2, 2<4 is true
Hence, not sufficient
Together: The first answer brings two options: either X<0 or 0<X<1 The second answer brings two options: either X<0 or 1<X
X cannot be both greater than 1 and smaller than one, hence it is negative. Answer C



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Re: 700 LEVEL QUESTION [#permalink]
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03 Aug 2010, 12:05
vouzico wrote: I'd say C:
The question is: is X>0 ?
1) X > X^3
X can be negative: If X=5, 5 > 75 is true X can be positive: If X=0,3 0,3 > 0.027 is true
Hence, not sufficient
2) X < X^2
X can be negative: If X=5, 5<25 is true X can be positive: If X=2, 2<4 is true
Hence, not sufficient
Together: The first answer brings two options: either X<0 or 0<X<1 The second answer brings two options: either X<0 or 1<X
X cannot be both greater than 1 and smaller than one, hence it is negative. Answer C I thought a similar thing at first, however on closer inspection I noticed that the original question mentions that X is an integer  therefore we can eliminate the cases where 1<X<1
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Re: 700 LEVEL QUESTION [#permalink]
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03 Aug 2010, 13:19
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ezhilkumarank wrote: My attempt:
Is integer X positive?
1. X > X^3
A number is greater than number raised to an odd powers implies that the number is an negative integer since a number raised to an odd power would retain its sign.
Ex:
2 > (2)^3
Hence X is negative. Sufficient
2. X < X^2
A number raised to an even power would mask its sign. Hence X^2 would always be positive.
Ex :1 2 < (2)^2
Ex :2 3 < 3^2
Hence X can be either positive or negative.
Insufficient
Answer is A is alone sufficient to solve this problem. What about 1/2 ? 1/2 > 1/8 the answer should be E stmt 1 ==> x>1 and 0<X<1 stmt 2 ==> X<0 and X>1



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Re: 700 LEVEL QUESTION [#permalink]
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03 Aug 2010, 13:26
mehdiov wrote: What about 1/2 ?
1/2 > 1/8
the answer should be E
stmt 1 ==> x>1 and 0<X<1
stmt 2 ==> X<0 and X>1 The questions says that X is an integer. No need to check for x=1/2. Answer is A.



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Re: Is integer X positive? 1. X > X^3 2. X < X^2 I was [#permalink]
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23 Apr 2013, 10:01
A)\(x > x^3\) in case 0 < x < 1 or if x < (1) but given x is integer so x is ve number sufficient B) \(x < x^2\) x<0 or if x>1, so x could be negative as well as positive. Not sufficient so A
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Re: Is integer x positive? [#permalink]
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23 Apr 2013, 11:08
I got it wrong.. i missed the word "integer" in the question.



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Re: Is integer x positive? [#permalink]
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28 Apr 2013, 03:07
shekar123 wrote: Is integer x positive?
(1) x > x^3 (2) x < x^2 (1) Sufficient. \(x>x^3\) is the same as \(x^3x<0\) or \(x(x^21)<0\). \(x^21>0\) for any integer \(x\) except 1, 0 1 which are not appropriate for us. So \(x<0\) (2) Insufficient. It could be 1 or 2 as well. The correct answer is A.
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Re: Is integer x positive? [#permalink]
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19 Jun 2013, 14:38
smyarga wrote: shekar123 wrote: Is integer x positive?
(1) x > x^3 (2) x < x^2 (1) Sufficient. \(x>x^3\) is the same as \(x^3x<0\) or \(x(x^21)<0\). \(x^21>0\) for any integer \(x\) except 1, 0 1 which are not appropriate for us. So \(x<0\) (2) Insufficient. It could be 1 or 2 as well. The correct answer is A. Answer A cannot be right. If you put in 1/2 or 2 the result will be the same. but different answers to the question! Sorry, my mistake oversaw the integer!



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Re: Is integer x positive? [#permalink]
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19 Jun 2013, 21:06
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shekar123 wrote: Is integer x positive?
(1) x > x^3 (2) x < x^2 You can use inequalities to solve this question or you can also solve it easily if you have a good understanding of the relation between x, x^2 and x^3 in various ranges. In fact, add \(\sqrt{x}\) to the list as well (though it is not needed in this question). Method 1: Inequalities (1) x > x^3 x^3  x < 0 x(x  1)(x + 1) < 0 1, 0 and 1 are the transition points. Inequality will hold when 0 < x <1 or x < 1. So x cannot be integer and positive both. Sufficient. (2) x < x^2 x^2  x > 0 x(x  1) > 0 0 and 1 are the transition points. Inequality will hold when x > 1 or x < 0. x can be an integer and either positive or negative. Not sufficient. Answer (A) Method 2: It is easy to see that A is enough if you understand the relation between x, x^2 and x^3. Look at the number lines below. Attachment:
Ques4.jpg [ 9.15 KiB  Viewed 2373 times ]
The green regions show the areas for which the relations hold. You can see that x^3 < x only for negative integer values (and some positive but non integer values) of x. Hence statement 1 is enough. Answer (A) Check out this link for a similar question that uses understanding of these relations (but the question is much tougher): http://www.veritasprep.com/blog/2011/08 ... question/
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Re: Is integer x positive? [#permalink]
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07 Apr 2015, 02:15
Hi Karishma,
Can you please explain how is x <1 or x > 1 My answer came x > 0 or x > 1. How to solve that inequality??



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Re: Is integer x positive? [#permalink]
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07 Apr 2015, 14:45
Hi All, This question can be approached in a couple of different ways, but you might find that using Number Properties and TESTing VALUES is a pretty fast way to get to the answer. We're told that X is an INTEGER. We're asked if it is POSITIVE. This is a YES/NO question. Fact 1: X > X^3 I'm going to TEST VALUES to prove a pattern... IF.... X = 1 X is NOT > X^3....so X CANNOT be 1 IF... X = 2 X is NOT > X^3....so X CANNOT be 2 IF.... X=3 X is NOT > X^3....so X CANNOT BE 3 As X increases, X^3 increases even more, so X CANNOT be any positive integer. Since the question asks if X is POSITIVE, we have the answer: NO, X is NEVER positive. Fact 1 is SUFFICIENT Fact 2: X < X^2 Here, we can TEST VALUES to prove that there are multiple answers.... IF.... X = 2 X IS < X^2 and the answer to the question is YES. IF.... X = 1 X is < X^2 and the answer to the question is NO. Fact 2 is INSUFFICIENT Final Answer: GMAT assassins aren't born, they're made, Rich
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Re: Is integer x positive? [#permalink]
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07 Apr 2015, 20:23
Shree9975 wrote: Hi Karishma,
Can you please explain how is x <1 or x > 1 My answer came x > 0 or x > 1. How to solve that inequality?? Check out this post to see how to solve inequalities: http://www.veritasprep.com/blog/2012/06 ... efactors/After you read this post, solve x(x  1)(x + 1) < 0 You will get that inequality will hold when 0 < x <1 or x < 1.
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Re: Is integer x positive? [#permalink]
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