If xy ≠ 0, is x an integer?

Question

(1) x^y is an integer.
(2) y is a prime number with y unique positive factors.

Kudos for a correct  solution .

KS15 · Answer

(1) x^y is an integer.Insufficient. x, y cab be 3 and 2 OR x, y can be 1/2 and -1
(2) y is a prime number with y unique positive factors.Insufficient. Value of x not given
Using both, x,y can be 2 and 3 OR \sqrt{3} and 2.
Answer E

TheKingInTheNorth · Answer

If xy ≠ 0, is x an integer?

(1) x^y is an integer.
(2) y is a prime number with y unique positive factors.

statement 1 not sufficient 
x^y = only possible when x is integer and y is +ve 
but when x is fraction in the form 1/x and y is -ve then only x^y is an integer holds true .

hence not possible . Note that other form of fraction for x will not hold true like 2/3, 3/4 etc .

Statement 2: gives information only about y not x

and that too y is prime with y unique positive factors. 
only possible value of y is 2

not sufficient

together 
y =2 (from 2)
and x^y must be an integer (from 1)

Hence x is an integer .

C ans

harishbiyani8888 · Answer

Correct answer is C

statement one is insufficient.

Here we do not know whether x is integer or if even y is integer. ex. 2^2 = integer and (1/2)^-2 = integer. SO x may or may not be an integer

Statement 2 is insufficient : we can infer that y is 2. So this tells us nothing about x.

Combine statement 1 and 2,

y =2 (positive integer) for x^2 to be integer , x has to be an integer.

stonepam · Answer

KS15: y is 2 so it can't be E.. Correct answer is C.

KS15 · Answer

But x,y can be 3,2 OR \sqrt{3},2 right?

emeraldweapon · Answer

(1). Lets say x = 1/2 and y = -1 => X^y = (1/2)^-1 = 2, which is an integer while x =1/2 is not => Insufficient
(2). Ask about x but provide info. about y, which is 2 => Insufficient

Together, y = 2 => X^2 is an interger <=> x is an integer

Hence, C

GMATinsight · Answer

Question  : If xy ≠ 0, is x an integer?

Statement 1 : x^y is an integer. 
Case 1: x =  \sqrt{2} , y = 2 and x^y =  (\sqrt{2})^2 = 2  i.e. x is NOT an Integer
Case 2: x = 1, y = 1 and x^y = 1 i.e. x is an Integer
NOT SUFFICIENT

Statement 2 : y is a prime number with y unique positive factors. 
Every prime number has 2 factors only
i.e. y = 2
Nut no information about x so
NOT SUFFICIENT

Combining the two statements : 
y = 2
Case 1: x =  \sqrt{2} , y = 2 and x^y =  (\sqrt{2})^2 = 2  i.e. x is NOT an Integer
Case 2: x = 1, y = 2 and x^y = 1 i.e. x is an Integer

NOT SUFFICIENT

Answer: option E

Bunuel · Answer

MANHATTAN GMAT OFFICIAL SOLUTION:

The question is asking whether x is an integer. Glancing at the statements, we can see that statement (2) only involves y, so it cannot be sufficient. (All we are told in the stem is that xy is not equal to 0, another way of saying that neither x nor y is equal to 0. That’s not a lot of information.) So we can rule out B and D without even analyzing (2) closely.

Statement (1) tells us that x^y is an integer. This does not guarantee that x is an integer. Of course, it could be. If y = 1, for instance, then x^y = x, so if x^y is an integer, then x is as well. However, if y = -2, then x could be 1/2, which is not an integer.1/2 raised to the -2 power is 4. So we can rule out A.

Now, put the two pieces of information together. We are told in (2) that y is a prime number with y unique factors. But every prime number has just 2 unique positive factors (1 and itself), so y must be 2. Combining this fact with the other statement, we know that x^2 is an integer. Does this tell us whether x is an integer? Of course, x could be an integer (2^2= 4), but the question is really whether x has to be an integer. The answer is no. After all, x^2 could equal 3. Then x would be equal to the square root of 3. Knowing that the square of x is an integer does not guarantee that x itself is an integer.

The correct answer is E.

bumpbot · Answer

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If xy ≠ 0, is x an integer?

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If xy ≠ 0, is x an integer?

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