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09 Sep 2019, 21:04
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E
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Difficulty:
45%
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48% (00:48) correct
52%
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wrong
based on 128
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Is X^N an integer?
(1) X is an integer
(2) N is an integer
Updated on: 10 Sep 2019, 23:19
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.
Last edited by EncounterGMAT on 10 Sep 2019, 23:19, edited 1 time in total.
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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
(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
09 Sep 2019, 22:04
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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.
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.
