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Is X^N an integer? (1) X is an integer (2) N is an integer
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09 Sep 2019, 21:04
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Competition Mode Question Is X^N an integer? (1) X is an integer (2) N is an integer
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Is X^N an integer? (1) X is an integer (2) N is an integer
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Updated on: 10 Sep 2019, 23:19
Is X^N an integer? (1) X is an integer (4)^1/2 = 2 (integer), 4^2 = 16 (integer) but (4)^2 (not integer).................INSUFFICIENT (2) N is an integer (1/2)^2 = i/4 (not integer) and 2^2= 4 = integer.............different answers possible......INSUFFICIENT (1) + (2) 2^1 = integer but 2^1 = not an integer. INSUFFICIENT IMO answer is option E
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Originally posted by EncounterGMAT on 09 Sep 2019, 22:01.
Last edited by EncounterGMAT on 10 Sep 2019, 23:19, edited 1 time in total.



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Re: Is X^N an integer? (1) X is an integer (2) N is an integer
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09 Sep 2019, 22:04
we are to determine if X^N is an integer. From statement 1, we know that X is an integer. This is however insufficient since we don't know the value of N. If N is an integer, then X^N will be an integer, but if N is not an integer, say 0.5 and N is 3, then 3^0.5 is not an integer.
From statement 2, we know that N is an integer. Since no information is given in relation to X, there are infinite possibilities of X^N, some of which are integers with others not integers. Statement 2 is therefore not sufficient.
1+2 is sufficient because we know X and N are both integers, hence X^N will always be an integer.
The answer is therefore C.



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Re: Is X^N an integer? (1) X is an integer (2) N is an integer
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09 Sep 2019, 22:37
(1) X is an integer N can take any value integer or non  integer. a. N is an integer → \(X^N\) is an integer. Example X = 2, N = 1, 2, 3 and so on. YES b. N is non – integer → \(X^N\) is non  integer. Example X = 2, N = 0.1, 0.2, 0.5 and so on. NO INSUFFICIENT. (2) N is an integer X can take any value integer or non  integer. a. X is an integer → \(X^N\) is an integer. Example N = 2, X = 1, 2, 3 and so on. YES b. X is non – integer → \(X^N\) is non integer. Example N = 2, X = 0.1, 0.2, 0.5 and so on. NO INSUFFICIENT. Together 1) and 2) Since both are integers Case ‘a’ of both statements suffices YES condition. SUFFICIENT. Answer (C).
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Re: Is X^N an integer? (1) X is an integer (2) N is an integer
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10 Sep 2019, 01:39
#1 value of N not know insufficient as ve integer value of N will be fraction insufficient #2 N is an integer ; value of X not know insufficeint from 1&2 value of sign of x & n not know insufficient IMO E
Is X^N an integer?
(1) X is an integer (2) N is an integer



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Re: Is X^N an integer? (1) X is an integer (2) N is an integer
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10 Sep 2019, 04:01
Quote: Is \(X^N\) an integer?
(1) X is an integer (2) N is an integer rule: "integer" = {positive, negative or zero} (1) X is an integer: \(X,N=(2,1):X^N=2^1=2=integer…X,N=(2,1):X^N=2^{(1)}=0.5=not.integer\) (2) N is an integer: \(X,N=(2,1):X^N=2^1=2=integer…X,N=(2,1):X^N=2^{(1)}=0.5=not.integer\) Answer (E)



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Is X^N an integer? (1) X is an integer (2) N is an integer
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Updated on: 11 Sep 2019, 08:58
Analyzing the question:Note that x does not have to be an integer for this to be sufficient. For example, we may have x = sqrt(2) and N be any even number, and this would be sufficient. Also, N = 0 is automatically sufficient if x cannot be 0. Statement 1:Without knowing N this is insufficient. N can be 1/2, which is square of x. There's also the possibility that N is a negative integer. Statement 2:x can be sqrt(2) and N=1. Insufficient. Combined:Still insufficient as we can let N = 1 and x be any integer greater than 1 to create a fractional result. Answer is E.
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Re: Is X^N an integer? (1) X is an integer (2) N is an integer
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10 Sep 2019, 13:41
Both statements are not sufficient as for X to the power of N to be an integer, we need X to be an integer and N to be a positive integer. From the given information, N can be either positive or negative and statement 1 is anyway not sufficient.
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Re: Is X^N an integer? (1) X is an integer (2) N is an integer
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10 Sep 2019, 21:21
Clearly statement 1,2 are not sufficient exclusively If we consider both, for x=2, n=3 .....x^n is integer but if n=2 then x^n is not integer SO OA:E



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Is X^N an integer? (1) X is an integer (2) N is an integer
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10 Sep 2019, 22:31
Bunuel wrote: Competition Mode Question Is X^N an integer? (1) X is an integer (2) N is an integer Is X^N an integer? (1) X is an integer \(2^2\) is an integer \(2^{2}\) is not an integer NOT SUFFICIENT (2) N is an integer \(2^2\) is an integer \(2^{2}\) is not an integer NOT SUFFICIENT Combining (1) & (2) \(2^2\) is an integer \(2^{2}\) is not an integer NOT SUFFICIENT IMO E
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Re: Is X^N an integer? (1) X is an integer (2) N is an integer
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30 Sep 2019, 19:13
Is X^N an integer?
(1) X is an integer N could be negative  which leads to a fraction. (2) N is an integer N could still be negative  which leads to a fraction.




Re: Is X^N an integer? (1) X is an integer (2) N is an integer
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30 Sep 2019, 19:13






