Is X^N an integer? (1) X is an integer (2) N is an integer

Question

Competition Mode Question

Is X^N an integer?

(1) X is an integer
(2) N is an integer

EncounterGMAT · Answer

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

eakabuah · Answer

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.

unraveled · Answer

(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).

Archit3110 · Answer

#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

exc4libur · Answer

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)

TestPrepUnlimited · Answer

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.

vaish2205 · Answer

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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madgmat2019 · Answer

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

Kinshook · Answer

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

djmobley · Answer

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.

Is X^N an integer? (1) X is an integer (2) N is an integer

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GMAT Data Sufficiency (DS) Questions

Is X^N an integer? (1) X is an integer (2) N is an integer

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