IMAT 2020 Q3 [Dotted Paper]

A piece of paper is laid on a table in landscape orientation (i.e. the longer side running left to right and the shorter side running top to bottom).

This piece of paper is then folded in half four times, alternately by moving the left hand side across over the right hand side and folding, and by moving the top half down over the bottom half and then folding. After each fold a dot is made with a pen in the centre of the face showing on the table.

After the four folds and four dots, the paper is unfolded in the reverse sequence and is then turned over so that the four dots are showing.

What is the pattern of the dots on the paper? (Dotted lines represent the fold marks)

image

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Simple steps to solve word problems:

  • Underline key information
  • Determine what they are trying to ask, and what you will need to solve it
  • Eliminate any non-essential information
  • Draw a picture, graph, or equation
  • In moments of high stress like exam taking, always work with the paper they give you to avoid careless mistakes.
  • Solve.

This is a question where I encourage you to get creative, in the exam you are given a few blank sheets, so why not do some practice folds on them? I wouldn’t recommend ripping or de-stappling anything unless you read the rules and are certain but you can certainly make a few practice folds while they are still in the booklet. When reviewing these questions (right now! as you are trying to figure out how to solve this in retrospect after finishing your practice), actually take a piece of paper and follow along. First, take the left side of the paper in your left hand and fold it over to the right. Put a dot in the very centre of the paper and label it 1. Next, take the top half and fold it downwards, label a 2. Repeat left over to right for dot 3, and top to bottom for dot 4.

Now, how can we solve this faster and easier for the exam?

The first fold is the easiest that can be down in your head, you must have a dot in the middle of half the page. See the image above, the dot labelled first fold should be easy to do in your head because it is just centred if the paper had a singular fold (left over right). Why is this important? Compare B with all other answer options, this essential first dot is not found on any other paper. By just doing one single step, we can eliminate every other option and simplify the question infinite times. You will also notice that no other dots from B match any other dots from another page, so even if you weren’t sure after one fold, any other fold you make would uniquely match with B and B only.

\fcolorbox{red}{grey!30}{Therefore B is the correct answer. }