Why is option D the correct answer to question 7? Quantity A is given as 2x, and it is evident that x is an obtuse angle. Therefore, 2x would exceed 180 degrees. Consequently, option A, which asserts that Quantity A is greater, should be correct.
Regarding question 12, could we also consider the reverse to be true? Specifically, can an equilateral triangle be classified as an isosceles triangle? I would appreciate a brief explanation addressing both perspectives.
In question 17, can we express the inequality as “3/√2 < k < 13/√2,” which translates to “2.12 < k < 9.19”? Since k must be an integer, this simplifies to “3 < k < 9,” leading to the conclusion that 9 - 3 = 6.
Hello,
Firstly, I sincerely apologize for the delay. In recent days, we Iranians have been occupied with preparations for our New Year celebration, Nowruz.
Secondly, regarding the first question I asked, why do you claim that x is not obtuse? As we can observe, it exceeds 90 degrees!
Thirdly, regarding the second question, when it states “COULD BE,” does it imply that if the third side of an isosceles triangle is also equal to the other two sides, the triangle would then become equilateral?
Additionally, if we want to consider the reverse, we can state that since all sides of an equilateral triangle are equal, it will ALWAYS qualify as an isosceles triangle.
Lastly, how did you determine that k equals 7 in my calculation? I calculated the range to be between 3 and 9, which means it could also be 4, 5, 6, or 8, not just 7.
Are you saying that we should never simply accept the image as it’s shown to us? That we need to explore all the possible ways it could be interpreted or drawn? And does this apply only to Geometry, since that’s usually where we’re given images to work with? (However, it is quite challenging to explore all possible approaches within the limited timeframe, as it seems impractical.)
Also, about the range, yes, the first step was just part of my calculation process. The final part, where 3 ≤ k ≤ 9, means the range should be calculated as 6, which is the correct answer.
Yes, unless the question explicitly states so. In some cases you can work with the problem assuming that it is to scale (even if technically it isn’t), but this needs to be done very carefully and is not common from my experience.
OK I see. The reason I pointed this out is that you initially said that 2.12 < k < 9.19, and the range there is just over 7.
Thank you for your explanation. So how are such questions typically phrased? What specific terms or words are used to indicate this (to rely exclusively on the visual representations of the questions)?
Yes, the first question I asked. So could the question explicitly clarify whether we should focus on the figure or not for scaling? because I have never encountered such a question before!
