sandy wrote:
Explanation
Translate the question and answer choices into algebra.
You are given that \(x - y = 4\).
Choice (A) tells you that \(x + y = 4\), and you can solve these equations simultaneously by stacking them and adding to get 2x = 8, x = 4 and y = 0.
Choice (A) is sufficient and correct.
Choice (B) tells you that \(x^2 - y^2 = 16\), and can be factored: \(x^2 - y^2 = (x + y)(x - y) = 16\). You are given that \((x - y) = 4\), so (x + y) must also equal 4 and for that to happen, x = 4 and y = 0.
Choice (B) is also sufficient and correct.
Choice (C) states \((x - y)^2 = 16\). This is simply the result of squaring what you were already given and you have no way to determine what the values of x
and y are, making this choice incorrect.
Choices (D) and (F) are inequalities, which means there will be multiple numbers that can work with the criteria given; eliminate both choices.
Choice (E) tells you that the greater number is 4. Since x - y = 4, that now means the smaller number must be 0, making choice (E) sufficient.
Finally, choice (G) states xy = 0, so at least one of the numbers must be 0. Since you were also given x – y = 4 and that neither number is negative, this means the other number must be 4. Choice (G) is sufficient and correct.
As the question stated that we have to Indicate all possible values not values which must be true,,,, so why we don't pick the option,C,D
C. The square of the difference between the numbers is 16. (if X=0, Y=4 ,,,,difference between x n y is -4 so -4^2=16
D.The sum of the squares of the numbers is greater than 8. (if X=0, Y=4 ,,,,Sum of 0^2+4^2=16 which is greater than 16
kindly guide me where I'm taking these concepts in wrong way