If z is an integer, is y an integer?

Question

(1)  y^2-z=0 
(2)  y
eq{1}

saswata4s · Answer

(1)
Suppose z = 3;
Then y = ±√3 = Not integer

again, suppose z= 4;
Then y = √4 = ±2 = Integer
Hence, Insuff.

(2) y≠1; Consider y = ±√3 or y = ±2
conditions in (1) still hold true. Insuff.

(1) & (2) together,
conditions in (1) still hold true. Insuff.
Ans: E.

rahul16singh28 · Answer

Hi  chetan2u ,

From Stmnt 1:  z =  y^2 , y can be  \sqrt{3} ,  \sqrt{5} 
From Stmnt 2: y # 1.. Insufficient

Combined.. Not Sufficient.. So E.

amanvermagmat · Answer

(1) y^2 - z = 0 or y^2 = z
This tells us that z is a non negative integer, but we cannot say anything about y. 
Here y will be an integer if z is a perfect square, else not. Insufficient.

(2) y is not equal to 1. This doesnt tell us whether y is an integer or not. Insufficient.

Combining the two statements, y=√z and y is not equal to 1. Still there are multiple possibilities. We can have z=9, then y can take two values: 3 or -3 (integer values). But if z =8, then y = √8 or -√8 (non integer values). So insufficient.

Hence  E answer

If z is an integer, is y an integer?

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If z is an integer, is y an integer?

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