Aptitude | Data Sufficiency | Question 1

Following instructions are to be used throughout the quiz:

Each of the questions given below consists of a statement and/or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is/are sufficient to answer the given question.
Read both the statements and Give answer
(a) if the data in Statement I alone is sufficient to answer the question, while the data in Statement II alone is not sufficient to answer the question.
(b) if the data in Statement II alone is sufficient to answer the question, while the data in Statement I alone is not sufficient to answer the question.
(c) if the data in each Statement I and Statement II alone is sufficient to answer the question.
(d) if the data even in both Statements I and II together are not sufficient to answer the question.
(e) if the data in both Statements I and II together are necessary to answer the question.

If x,y are integers, then (x² + y²)^1/2 is an integer?
I) x² + y² is an integer
II) x² – 3y² = 0
(A) A
(B) B
(C) C
(D) D
(E) E

Answer: (B)
Explanation: Statement 1:
x² + y² is an integer
Since x and y are integer x²+y² can be any real number which may not be a perfect square so statement 1 alone cant prove whether (x²+y²)^(½) is an integer or not.
Statement 2:
x²– 3y² = 0
=>x²+y²-4y²=0
=>x²+y²=4y²
=> (x²+y²)^(½)= 2y
Which is an integer because y is an integer.

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