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Is x an integer greater than 1?
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Updated on: 30 Jan 2017, 09:20
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21% (01:45) correct 79% (01:21) wrong based on 145 sessions
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Is x an integer greater than 1? (1) The cube of x is a positive integer. (2) The reciprocal of x is less than 1.
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Originally posted by duahsolo on 25 Oct 2016, 15:12.
Last edited by Bunuel on 30 Jan 2017, 09:20, edited 3 times in total.
Edited the OA.



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Re: Is x an integer greater than 1?
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25 Oct 2016, 15:45
duahsolo wrote: Is x an integer greater than 1?
(1) The cube of x is an positive integer. (2) The reciprocal of x is less than 1. Statement 1: x^3 =8, x =2 Yes x^3=2, x=cuberoot(2) No Insufficient Statement 2: 1/x =0.5 Then x=2 Yes 1/x = 0.6667 x=1.5 No Insufficient Statement 1&2: If x= 2, then x^3 = 8 and 1/x=0.5 Yes If x= cuberoot(2), then x^3 = 2 and 1/x will always be less than 1. No Again insufficient IMO E duahsolo : Please confirm the answer Sent from my iPhone using GMAT Club Forum mobile app



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Re: Is x an integer greater than 1?
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25 Oct 2016, 21:08
duahsolo wrote: Is x an integer greater than 1?
(1) The cube of x is an positive integer. (2) The reciprocal of x is less than 1. Hi duahsoloCould u confirm your OA Combining both statements X could be 2>YES X is integer>1 or X=2^1/3> NO X is NOT integer>1 insuff.. Ans E



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Re: Is x an integer greater than 1?
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25 Oct 2016, 22:02
The cube of x is an positive integer let x=1 , its cube is still positive integer, which is 1 answer is NO x=2 answer is YES
The reciprocal of x is less than 1 let x=2 its reciprocal is less than 1 as it will be negative
combining answer is C because on combining , this rules out the option x<=1



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Re: Is x an integer greater than 1?
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26 Oct 2016, 00:08
rohit8865 wrote: duahsolo wrote: Is x an integer greater than 1?
(1) The cube of x is an positive integer. (2) The reciprocal of x is less than 1. Hi duahsoloCould u confirm your OA Combining both statements X could be 2>YES X is integer>1 or X=2^1/3> NO X is NOT integer>1 insuff.. Ans E Hi rohit8865, I can confirm that the OA is (C)
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Re: Is x an integer greater than 1?
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26 Oct 2016, 00:09
acegmat123 wrote: duahsolo wrote: Is x an integer greater than 1?
(1) The cube of x is an positive integer. (2) The reciprocal of x is less than 1. Statement 1: x^3 =8, x =2 Yes x^3=2, x=cuberoot(2) No Insufficient Statement 2: 1/x =0.5 Then x=2 Yes 1/x = 0.6667 x=1.5 No Insufficient Statement 1&2: If x= 2, then x^3 = 8 and 1/x=0.5 Yes If x= cuberoot(2), then x^3 = 2 and 1/x will always be less than 1. No Again insufficient IMO E duahsolo : Please confirm the answer Sent from my iPhone using GMAT Club Forum mobile appHi acegmat123, I can confirm that the OA is (C)
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Re: Is x an integer greater than 1?
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09 Jan 2017, 09:50
Bunuel wrote: Is x an integer greater than 1?
(1) The cube of x is an positive integer. (2) The reciprocal of x is less than 1. (1) x=2 > \(x^3=8\), x=\(\sqrt[3]{2}\) > \(x^3 = 2\) or x=1, \(x^3 = 1\) Insufficient. (2) x=4, 1/x=1/4 < 1 x=1/2, 1/x = 2 < 1 x=\(\sqrt[3]{2}\), 1/x = 1/\(\sqrt[3]{2}\) < 1 x=2, 1/x = 1/2 < 1 Insufficient (1) & (2) We can discard negative values and 1 but still have positive irrationals and integers >1. E.



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Re: Is x an integer greater than 1?
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10 Jan 2017, 08:59
ANS (E) Q) X>1 ? (1) X^3 IS AN INTEGER X=2, 2^3= 8 X=1, 1^3=1 NOT SUF. (2) RECP >1 1/2 <1 SUF. 2 <1 , RECIPROCAL = 1/2< 1 HENCE NOT SUFF 1 AND 2 COMBINED NO UNIQUE ANSWER. 
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Re: Is x an integer greater than 1?
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11 Jan 2017, 09:49
Bunuel wrote: Is x an integer greater than 1?
(1) The cube of x is an positive integer. (2) The reciprocal of x is less than 1. From option 1 we can identify that x is positive and from option 2 we can reach the conclusion that x >1 (if x is positive) x<1 (x is negative) So combining 1 & 2 we can say that x>1 so Answer is C



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Re: Is x an integer greater than 1?
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11 Jan 2017, 11:09
Bunuel wrote: Is x an integer greater than 1?
(1) The cube of x is an positive integer. (2) The reciprocal of x is less than 1. (1) if x=1 then NO if x=2 then YES insuff (2) 1/x<1 (1x)/x<0 thus x<0 or x>1 if x= 2 then NO if x= 2 then YES not suff Combining we know 3 √x is positive integer(from (1) ) and x>1 from (2) thus x>1 but if x= cube rt 3 then NO insuff Ans E



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Re: Is x an integer greater than 1?
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11 Jan 2017, 11:53
Bunuel wrote: Is x an integer greater than 1?
(1) The cube of x is an positive integer. (2) The reciprocal of x is less than 1. Statement1: x^3 can be equal to 1 or greater than 1. Not Sufficient. Statement2: 1/2 =0.5 1/2 =0.5 Not Sufficient. E.



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Re: Is x an integer greater than 1?
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29 Jan 2017, 10:50
Bunuel wrote: Is x an integer greater than 1?
(1) The cube of x is an positive integer. (2) The reciprocal of x is less than 1. 1. It means X is positive but we don't know it is grater than 1 or 1 itself.So insuff 2.From this we can conclude that x can't be 1. Now we have X is positive, X can't be 1, X is a integer we can get X>1 C .suff.



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Re: Is x an integer greater than 1?
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29 Jan 2017, 12:13
Hi, as per me ans should be E.
From Statement 1: x can be = 4, x can be = Cube root(2), or x= 5, so insuff From Statement 2: again x can be = 4, x can be = Cube root(2), or x= 5, so insuff
From 1 + 2: x can be = 4, x can be = Cube root(2), so insuff. So ans: E



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Re: Is x an integer greater than 1?
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29 Jan 2017, 12:49
pandeyamit07 wrote: Hey sobby, I didn't get your answer as in statement 2, it's not given X is integer or not. Can you please explain this. Sent from my Redmi Note 3 using GMAT Club Forum mobile appOk..It is given reciprocal of x is less then 1 ...So any value above 1 will have its reciprocal less then 1... Now ,1 have reciprocal equal to 1 ..So we can discard 1 here...And reciprocal between 0 to 1 will be greater than 1...Discard that too.. We have negative values too in the set..So from statement 2 we can't conclude anything..It is in suff. Combining... From statement 1 we have x is positive integer only,and statement 2 tells it is not 1 atleast...So it is obvious that value of x will be all positive value greater than 1.. Sent from my HM NOTE 1LTE using GMAT Club Forum mobile app



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Re: Is x an integer greater than 1?
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29 Jan 2017, 21:24
sobby wrote: Bunuel wrote: Is x an integer greater than 1?
(1) The cube of x is an positive integer. (2) The reciprocal of x is less than 1. 1. It means X is positive but we don't know it is grater than 1 or 1 itself.So insuff 2.From this we can conclude that x can't be 1. Now we have X is positive, X can't be 1, X is a integer we can get X>1 C .suff. How do we get X as an Integer. Let's take X= Cube root of 4 Cube root of 4 has it's Cube as 4 (Satisfies 1) Reciprocal of Cube root of 4 is < 1 (Satisfies 2) X is Positive and greater than 1 but not Integer If we take X=3 Then Cube of 3 is Integer (Satisfies 1) Reciprocal if 3 is < 1 (Satisfies 2) X is Positive Integer greater than 1. Depending on how what we chose as X it can be Integer or not. So Why isn't the answer C. What am I missing here.



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Is x an integer greater than 1?
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30 Jan 2017, 11:53
Bunuel wrote: duahsolo wrote: Is x an integer greater than 1?
(1) The cube of x is a positive integer. (2) The reciprocal of x is less than 1. Edited the OA. It should be E. Hi Bunuel, if OA is E, can you please share where I am going wrong below ? Given x is an integer, St.1  (x^3) is >0. Put x=2. Yes. Put x=1. No. So, insufficient. St 2  (1/x) is < 1. If x is positive, x >1. If x is negative, x <1. So, insufficient. St.1 + St.2  Suppose x=2. (2^3) is +ve integer & (1/2) is less than 1. So, x is an integer >1. Suppose x=1. (1^3) is +ve integer. Reciprocal of x is not less than one. Can't take x=1. Combining st1 & 2, we have to take integer values of x>1 to satisfy both the statements. So, C.



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Is x an integer greater than 1?
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30 Jan 2017, 12:40
ajay2121988 wrote: Bunuel wrote: duahsolo wrote: Is x an integer greater than 1?
(1) The cube of x is a positive integer. (2) The reciprocal of x is less than 1. Edited the OA. It should be E. Hi Bunuel, if OA is E, can you please share where I am going wrong below ? Given x is an integer, St.1  (x^3) is >0. Put x=2. Yes. Put x=1. No. So, insufficient. St 2  (1/x) is < 1. If x is positive, x >1. If x is negative, x <1. So, insufficient. St.1 + St.2  Suppose x=2. (2^3) is +ve integer & (1/2) is less than 1. So, x is an integer >1. Suppose x=1. (1^3) is +ve integer. Reciprocal of x is not less than one. Can't take x=1. Combining st1 & 2, we have to take integer values of x>1 to satisfy both the statements. So, C. had the question asked that "Is integer x greater than 1?" then your solution is a valid one.. Hope this helps !!



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Re: Is x an integer greater than 1?
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31 Jan 2017, 01:01
deepayanc wrote: sobby wrote: Bunuel wrote: Is x an integer greater than 1?
(1) The cube of x is an positive integer. (2) The reciprocal of x is less than 1. 1. It means X is positive but we don't know it is grater than 1 or 1 itself.So insuff 2.From this we can conclude that x can't be 1. Now we have X is positive, X can't be 1, X is a integer we can get X>1 C .suff. How do we get X as an Integer. Let's take X= Cube root of 4 Cube root of 4 has it's Cube as 4 (Satisfies 1) Reciprocal of Cube root of 4 is < 1 (Satisfies 2) X is Positive and greater than 1 but not Integer If we take X=3 Then Cube of 3 is Integer (Satisfies 1) Reciprocal if 3 is < 1 (Satisfies 2) X is Positive Integer greater than 1. Depending on how what we chose as X it can be Integer or not. So Why isn't the answer C. What am I missing here. Hi deepayanc, Please refer the highlighted part. Since there is no unique answer, so the correct answer should be E.



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Re: Is x an integer greater than 1?
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25 Feb 2018, 18:43
Bunuel, what is the official solution of this problem?



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Re: Is x an integer greater than 1?
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25 Feb 2018, 23:59
futurephilantropist wrote: Bunuel, what is the official solution of this problem? Is x an integer greater than 1?Notice that we are not told that x is an integer. We should determine exactly that plus whether it's more than 1. (1) The cube of x is a positive integer > \(x^3 = positive \ integer\). This is true for any positive integer so x certainly could be an integer greater than 1 but not necessarily. For example: If x = 1 > the answer is NO. If \(x = \sqrt[3]{2}\) > the answer is NO. Not sufficient. (2) The reciprocal of x is less than 1 > 1/x < 1. This holds true for any value greater than 1 (not necessarily an integer) as well as any negative value. Not sufficient. (1)+(2) From (1) it follows that x is positive, so from (2) that x must be greater than 1 but x still could be an integer greater than 1 (for example 2) as well as some irrational number, which gives an integer when cubed (for example \(\sqrt[3]{2}\)). Not sufficient. Answer: E. Hope it's clear.
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Re: Is x an integer greater than 1?
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