500 PS #20

dunkin77 wrote:Hi,

I thought the answer is B) but turned out to be A) - Can anyone please explain??


If y ≠ 3 and is a prime integer greater than 2, which of the following must be true?
Ⅰ. x = y
Ⅱ. y = 1
Ⅲ. x and y are prime integers.
(A) None
(B) Ⅰ only
(C) Ⅱonly
(D) Ⅲonly
(E) Ⅰand Ⅲ

The question does not put any condition or Constraints on X, meaning X can take up any value . SO 1 and 111 ruled out . Y is not 1 by the question so 11 is also ruled out ..

thus A

from the question, $$y\ne3\ and\ y>2$$
let's analyse the statement i to iii.
I. x=y
from the question, there is no mention of X or its value, which means it could be 7, 0, -1 or 100.21. So, we don't know how if x is a prime integer or not.
Therefore, I is false or we can say I cannot be true

II. y=1
The value of y is said to be greater than 2.Hence, readers statement is false too. II is false.

III. x and y are prime integers.
True enough , Y is a prime integer as given in the question. But we cannot say that X is because we are not given any values for X. Thus, III is false

$$Therefore\ "None"\ is\ the\ correct\ answer.\ Hence\ Option\ A\ is\ very\ correct$$