I was hoping you could explain this problem for me? I got it from the beatthegmat.com practice bank. I'm confused, especially because I don't see where they get that 0 (1. Premise second slide) is positive integer x. I know that 0 is even but I thought it was not positive nor negative. In the third slide they change x to 4. Can you help on this problem?
You are right that 0 is even but that it is neither positive nor negative, and you're right that they shouldn't be using x=0 as a possible case because it violates the condition they've specified. Typo on BTG! But Statement 1 is still insufficient because y could be 0 (since we're not told that y is positive), so if you let x be any perfect square and let y be 0, you will satisfy Statement 1 and get a YES answer to the question; if, on the other hand, you let x and y be different things (like 1 and 3, for example, or 2 and 7), then you'll satisfy Statement 1 and get a NO answer. So Statement 1 gives you a maybe.
Statement 2 gives you a YES, DEFINITELY, because we can transform Statement 2 into 8x^2 = y^2, and then when we substitute 8x^2 in for y^2 in the original question, the question winds up saying "Is root(x^2 + 8x^2) an integer?"... in other words, is root(9x^2) an integer?...in other words, is 3x an integer? And yes, it is, since x itself is an integer.
You are right that 0 is even but that it is neither positive nor negative, and you're right that they shouldn't be using x=0 as a possible case because it violates the condition they've specified. Typo on BTG! But Statement 1 is still insufficient because y could be 0 (since we're not told that y is positive), so if you let x be any perfect square and let y be 0, you will satisfy Statement 1 and get a YES answer to the question; if, on the other hand, you let x and y be different things (like 1 and 3, for example, or 2 and 7), then you'll satisfy Statement 1 and get a NO answer. So Statement 1 gives you a maybe.
Statement 2 gives you a YES, DEFINITELY, because we can transform Statement 2 into 8x^2 = y^2, and then when we substitute 8x^2 in for y^2 in the original question, the question winds up saying "Is root(x^2 + 8x^2) an integer?"... in other words, is root(9x^2) an integer?...in other words, is 3x an integer? And yes, it is, since x itself is an integer.
