The next one from the 2017 Year 7 test, again from the calculator part. (Compare to this one, from the 2021 Year 9 test.)

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# WitCH 131: Toying With Us

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11 Replies to “WitCH 131: Toying With Us”

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The next one from the 2017 Year 7 test, again from the calculator part. (Compare to this one, from the 2021 Year 9 test.)

This question seems designed to eliminate students who are too clever.

It is kind of terrifying that this question slipped though their proof reading process – assuming there is one. @J.D. do you thank a clever student would see what was meant or freak out about the unaccounted for rectangles?

I wonder if they use psychometric analysis like VCAA to argue that the question didn’t disadvantage *any* students…

Which one(s) are the rectangles?

Assume the triangles on the top face are each connected to a square on the side faces.

The diagonal of these triangles, hence the length of the side squares, will be greater than the smaller side lengths which, according to the diagram, make the side lengths of other squares on the sides.

But then, similarly to other WiTCHES recently, the squares will not line up along the sides in the manner shown.

Hence, one set of “squares” (it doesn’t matter which) must be rectangles.

Yep, there are undoubtedly (non-square) rectangles. But, if some are non-square then why not all?

Why didn’t they just say rectangles, as that would include squares?

Because that would make too much sense, Cathy. But even then, I say that the question cannot be answered …

The diagram is drawn to scale (since there is no statement that it’s not, unless there is a global statement at the start of the question booklet like the one VCAA uses) so we must assume that the non-square rectangles that we can see are indeed non-square rectangles. But since we can’t see all of the sides, for all we know, some of those sides we can’t see have squares.

Because the question specifies that squares and triangles are used to cover the surface.

I therefore assume that somewhere between and of the “rectangles” are also squares.

My fractions do not include the squares on the two ends, which also need not be squares.

I think a clever student would notice that something was amiss. Initially they would assume they themselves had some misunderstanding. After some more thought, they might conclude that the question setter had made a mistake, depending on how much they trust the process and perhaps on personality factors. Then they would give the expected answer, counting all the rectangles as squares. Otherwise they might start thinking something like “Oh, it doesn’t say there are only squares and triangles. Maybe I need to determine how many of the rectangles are squares” (which is impossible).

Does “Its surface is covered in triangles and squares” exclude the possibility that the surface is also covered in (non-square) rectangles?

Nevertheless, as I commented earlier, “since we can’t see all of the sides, for all we know, some of those sides we can’t see have squares.” We cannot assume that all sides look the same, the question is impossible to answer. Someone at ACARA is a blockhead.

Obviously the question is screwed, every which way. But not being able to see the back (or base) of the thing is the least of the problems. One can make a good faith interpretation on this (while noting it is bad to have to do so), and still the question is screwed.