If z is a positive integer, is z^1/2 an integer?
(1) xz^1/2 is an integer.
(2) x = z^3
Taken together, the statements are still insu¢ cient. Since (2) gives you x
in terms of z, you can plug that into (1):
((z^3)(z))^1/2 = integer (z^4)^1/2 = integer
z^2 = integer
Knowing that z^2 is an integer is not enough to answer the question: we want
to know whether z itself is a perfect square. As is, z neednÂ’t even be an integer,
let alone a perfect square: it could be 2^1/2. It could be an integer, but for Data
Sufficiency, "could" isnÂ’t good enough.
My doubt is in the question it been mentioned that z is an integer, but this is being contradicted when both statements are taken together.
Where am I going wrong?
(1) xz^1/2 is an integer.
(2) x = z^3
Taken together, the statements are still insu¢ cient. Since (2) gives you x
in terms of z, you can plug that into (1):
((z^3)(z))^1/2 = integer (z^4)^1/2 = integer
z^2 = integer
Knowing that z^2 is an integer is not enough to answer the question: we want
to know whether z itself is a perfect square. As is, z neednÂ’t even be an integer,
let alone a perfect square: it could be 2^1/2. It could be an integer, but for Data
Sufficiency, "could" isnÂ’t good enough.
My doubt is in the question it been mentioned that z is an integer, but this is being contradicted when both statements are taken together.
Where am I going wrong?
