<p>Interesting note, the ambiguity of the question is ambiguous, no one here seems to be able to get everyone here to agree on a singular unambiguous interpretation of the problem. And it is possible for students to slip up on questions in English that are perfectly clear in other languages. Take the word love for instance, we only have one commonly used word for love. Now in ancient greek there were several different words, encompassing most needed definitions. Also don’t forget that english is the only language in which slim chance and fat chance mean the same thing, but wise man and wise guy are total opposites, a cliche I know, but still true.</p>
<p>The correct answer would be achieved in the following way:
4x3 + 2x12 + 2x8 + 25 = 77
Now, if we ignore the 25, 52 becomes the answer, so that is 2 possible answers. If instead the student assumes the answer is the sum of two times each of the side lengths + 25, the equation becomes 2x3 + 2x12 + 2x8 + 25 = 71, another possible answer. And in the latter case if the student forgets to add 25 he gets 46. That gives four out of the five answers can be reached by leaving out some information, or none of it. The last answer of 65 can only be reached by ignoring the inclusion of the height of the box. This last answer, is not excusable, but can be reached, by not going to far off course. </p>
<p>This reminds of a story, its veracity is unknown, about a company that was looking to expand operations and needed to decide between two applicants that they thought were roughly comparable. So the hiring manager gives them a test and calls them in the next day. He tells them that they scored equally well on the test, the exact same 9 problems right, and based on their right answers he can’t make a decision. So he tells them that the decision will be made based on the one question they both got wrong, one person wrote, I don’t know, the other wrote, I don’t know either. </p>
<p>While I don’t know if this story is true, it is telling that so much information can be gleaned from the wrong then the right ones. However, all this test tells us is the percentage of students who got the question absolutely right, not why they got it right or wrong in the case of the wrong students. </p>
<p>Also a student not good at arithmetic could easily improve his chances of getting it right through guessing. 8 and 12 are both about ten, 4 times ten is 40, plus an additional 25 is 65, adding numbers that end in 0 and 5 are fairly easy, and multiplication by 10 is very easy. With the fact that there is still some amount over, that narrows the choice down to two answers 71 and 77, which you have far better odds of guessing correctly then if you could chose between all five.</p>