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I'm guessing there is a typo and that \(y^2=x\) is actually statement 1.

(1) \(y^2=x\) [Insufficient] We are not told that y is an integer. If y is an integer, then x is not prime. Otherwise, y could be the square root of a prime such as \(\sqrt{2}\) (2) \(2x/x^2 = 1\) [Sufficient] From this statement, we can see that x is not zero. Multiplying both sides by \(x^2\), we get \(2x = x^2\). Dividing both sides by x, we are left with x = 2, which is a prime number.

My answer was C. Neither statement is sufficient: In stmt 1, "y" can be 0,1, or the square root of a prime as stated above. Multiple possibilities, not sufficient In stmt 2, "x" can be 1 or 2 and (2x / x^2) will equal 1. Multiple possibilities, not sufficient.

The problem never specified that x or y must be integers.

Statement 1 is insufficient: y^2=x If y is an integer then x is not prime. If y is not an integer like sqrt2,sqrt3…. then x is prime. So not sufficient. Statement 2 is sufficient: 2/x=1 So x is 2. Which is prime. So answer is B.
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I. y could be 1, giving us a NO answer to the question (since 1 is not prime), or it could be (2)−−−√, giving us a YES answer to the question (since 2 is prime). Insufficient.

II. If you cross-multiply this equation, you'll get 2x = x². There are two solutions to this equation 0 and 2, but we can rule out 0, because that would put 0 in the denominator of the fraction in the original form of the equation, and putting 0 in the denominator is not allowed; it is undefined.

Therefore, x must be 2, a prime, giving us a YES in answer to the question. Sufficient.
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I. y could be 1, giving us a NO answer to the question (since 1 is not prime), or it could be (2)−−−√, giving us a YES answer to the question (since 2 is prime). Insufficient.

II. If you cross-multiply this equation, you'll get 2x = x². There are two solutions to this equation 0 and 2, but we can rule out 0, because that would put 0 in the denominator of the fraction in the original form of the equation, and putting 0 in the denominator is not allowed; it is undefined.

Therefore, x must be 2, a prime, giving us a YES in answer to the question. Sufficient.

Hi! Just a small query please st1) doesnt matter at all y could be anything.......... ok? st2) can x as a variable be reduced.. as its an equation rather inequality.. and hence coming up B as an answer... please help in this.. thanks

We need to get if x is prime or not statement 1 => x=y^2 If y is an integer then x wont be prime ( Primes can never be factorised) Else if y=√2 then x=2 => Prime Hence since no clue of y is given => Not suff Statement 2 => 2x/x^2=1 here x can never be 0 as something /0 => not defined hence x^2=2x=> x=2 which is a prime number Therefore suff

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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