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Manager  G
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Is x an integer greater than 1?  [#permalink]

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Difficulty:   95% (hard)

Question Stats: 21% (01:45) correct 79% (01:21) wrong based on 145 sessions

### HideShow timer Statistics 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?  [#permalink]

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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

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Re: Is x an integer greater than 1?  [#permalink]

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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 duahsolo

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?  [#permalink]

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1
The cube of x is an positive integer
let x=1 , its cube is still positive integer, which is 1 answer is NO

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?  [#permalink]

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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 duahsolo

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?  [#permalink]

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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

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Hi acegmat123,

I can confirm that the OA is (C)
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Re: Is x an integer greater than 1?  [#permalink]

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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=$$\sqrt{2}$$ --> $$x^3 = 2$$ or x=1, $$x^3 = 1$$ Insufficient.

(2) x=-4, 1/x=-1/4 < 1
x=-1/2, 1/x = -2 < 1
x=$$\sqrt{2}$$, 1/x = 1/$$\sqrt{2}$$ < 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?  [#permalink]

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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?  [#permalink]

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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

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Re: Is x an integer greater than 1?  [#permalink]

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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
(1-x)/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?  [#permalink]

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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?  [#permalink]

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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?  [#permalink]

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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?  [#permalink]

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pandeyamit07 wrote:
Hey sobby, I didn't get your answer as in statement 2, it's not given X is integer or not.

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Ok..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..

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Re: Is x an integer greater than 1?  [#permalink]

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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?  [#permalink]

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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?  [#permalink]

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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.

then your solution is a valid one..

Hope this helps !!
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Re: Is x an integer greater than 1?  [#permalink]

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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?  [#permalink]

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Bunuel, what is the official solution of this problem?
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Re: Is x an integer greater than 1?  [#permalink]

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1
1
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 $$x = \sqrt{2}$$ --> 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 $$\sqrt{2}$$). Not sufficient.

Hope it's clear.
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