If x and y are non-zero integers, Is x

Question

If x and y are non-zero integers, Is x < y ?
(1)  x = \frac{1}{y^{2}} 
(2) x + y = 0

nick1816 · Answer

Statement 1- x=\frac{1}{y^2} Suppose x1 or y>1 but if y>1, x can never be an integer. Hence, if x=\frac{1}{y^2} and x and y are integers, x can never be smaller than y. Sufficient Statement 2 - Case 1- x=2; y=-2 Case 2- x=-2; y=2 Insufficient

Codebug4it · Answer

Answer:  Option A

Option 1:  
x = 1 / (y ^ 2)
=> x * (y ^ 2) = 1
=> As x and y can only be non-zero integers,  This implies x has to be '1' and y can be '1' or '-1'

In both the scenarios, x is not less than y. Hence it is sufficient to answer the question.

Sufficient

Option 2: 
 x + y = 0
=> x = -y
=> if x is negative then y is positive -> x < y
=> if x is positive then y is negative -> x > y

Insufficient

GMATinsight · Answer

Question: Is x < y?

Statement 1 :  x = 1/y^2

for any negative value of y, x will be positive hence x > y  i.e. x is NOT less than y

For positive integer values of y
at y = 1, x = 1  i.e. x is NOT less than y 
at y = 2, x = 1/4  i.e. x is NOT less than y

CONSISTENT Answer hence

SUFFICIENT

Statement 2 : x + y = 0

i.e. one of x and y is  NOT SUFFICIENT

Answer: Option A

WheatyPie · Answer

In your second example, x is not an integer. That example shouldn't be considered.

JeffTargetTestPrep · Answer

x and y are nonzero integers.

We need to answer the question:

Is x < y ?

Statement One Alone:

=> x = 1/y^2

(x)(y^2) = 1

The product of two integers is equal to 1 if and only if both integers are equal to 1 or both are equal to -1.

Since the integer y^2 cannot be negative, it must be true that:

x = 1

y^2 = 1 => y = 1 OR y = -1

If x = 1 and y = 1, then the answer is No. If x = 1 and y = -1, then the answer is still No. Since we have a definite No answer to the question, statement one is sufficient. Eliminate answer choices B, C, and E.

Statement Two Alone:

=> x + y = 0

If x = 1 and y = -1, then the answer is No. Whereas, if x = -1 and y = 1, then the answer is Yes. Statement two is not sufficient.

Answer: A

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If x and y are non-zero integers, Is x < y ? (1) x = 1y2 (2) x + y = 0

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