GMATinsight wrote:
Another point, whether you take (3, 4, 5) or (5, 12, 13) it fit in both cases. and the forward application doesn't approve of backward application as well. (1 is a natural no. doesn't mean that a natural no. has to be 1)
I'm afraid I don't understand your reply. In your first post, you said that when "the side of a right angle triangle is a prime number then other two sides will be" x and y. That is, you said we can determine the other two sides from one side, when the length of that one side is prime. That's not true, but if a test taker believed it was, he or she might answer questions incorrectly on the GMAT - for example, a DS question like the following:
If the lengths of the three sides of a right triangle are integers, what is the perimeter of the triangle?
1. The length of one side is 5
2. Two of the lengths are prime numbersA test taker who thinks that a single prime length is sufficient to determine the other two will think Statement 1 is sufficient, and will pick A, which is not the right answer - the answer is E, since the triangle might be a 3-4-5 or 5-12-13 triangle. I will always post a clarification if an expert here posts something which might be misinterpreted, and which might lead a test taker to answer test questions incorrectly, and I'd always be grateful to anyone who posts a clarification of one of my posts if I were ever to make an error.
I also don't understand why you think I confused your statement with its converse (what you're suggesting in your comment about natural numbers). I did not. Nor do I understand why you consider it relevant that the 3-4-5 triangle fits your formula, since we don't find the lengths 3 and 4 by plugging in '5', but regardless there are other triangles with a prime length that do not satisfy those formulas - the 8-15-17 triangle, for example.
GMATinsight wrote:
You seem of have less understanding of the word "OPINION"
I hope you prove me wrong by bringing ONE question from authentic source of GMAT questions if you have enough exposure of GMAT.(Refer
OG, GMAT PREP etc.)
I don't think it often is a matter of opinion whether a question falls within the scope of the GMAT. It's not clear to me precisely why you think this question is out of the scope of the test. I agree with you when you say, referring to your formulas, that "GMAT Doesn't expect such tricks from students." That seemed to me the only reason you described this question as "unsuitable" for the test. But those formulas aren't at all necessary here, so I disagreed with your initial premise. The main mathematical issue in this question, when solving it using the difference of squares factorization, is recognizing that when b > c > 0, and b and c are positive integers, the equation (b+c)(b-c) = 121 has only one possible solution. If you want to see an official question that relies on very similar logic, see this one from GMATFocus:
if-x-and-y-are-integers-such-that-x-y-0-what-is-x-156464.html