Figure series, mirrors, embedded shapes and paper folding.
About Dot Situation
A dot situation question shows several outlines crossing one another with a dot placed somewhere among them, and asks which of the outlines enclose the dot. It is a question about position rather than about shape, and the answer is decided by the geometry: the dot is inside a given outline or it is not.
What you need to understand
An outline divides the plane into an inside and an outside. Which side the dot falls on is the whole question.
The interesting place for a dot is where two or three outlines overlap, because there the answer is a combination rather than a single letter.
Read the figure one outline at a time. Trying to see all the regions at once is what makes these questions look harder than they are.
A line has to be followed all the way round. Two outlines cross, and what matters is which side of the line the dot is on after the crossing.
The dot being near a line tells you nothing. Only the side counts, and a dot a long way from a line can still be inside it.
The outermost outline is easy to settle, so start there. It removes one option from consideration immediately in most figures.
How to work through these questions
Pick one outline and trace it round the whole figure with your eye, starting from any point.
Ask where the dot sits relative to that line: on the inside of the closed curve, or the outside.
Do the same for the second outline, and then the third. Keep a note of your answers rather than holding them in mind.
Combine the answers. The dot is in those outlines and outside the others, and the combination is the answer.
Check the result against the figure once more, looking at the outline you found hardest.
Reject any option that names an outline whose line the dot can plainly be seen to be on the far side of.
Mistakes that cost marks
Judging by which line is nearest the dot instead of which side of the line the dot is on.
Reading only part of an outline before deciding, so that a crossing is missed.
Assuming the dot is in every outline it lies between, when it may be outside the outermost one.
Answering with a single outline when the dot falls in an overlap of two.
Losing track of which line belongs to which letter in a figure where the outlines cross several times.
Deciding by the size of the region the dot appears to be in, which has nothing to do with the answer.
Worked example
A figure has three outlines labelled A, B and C, crossing one another, with a dot placed in the region where A and C overlap and B does not reach.
Take outline A first and follow it round. The dot lies on the inner side of it, so the dot is inside A.
Take outline B. The dot is on the outer side of B, which can be seen by following B round past the dot.
Take outline C. The dot lies on the inner side of it, so the dot is inside C.
Combine the three answers: inside A, outside B, inside C.
The answer is A and C.
Answer: A and C
Practice questions with answers
A few Dot Situation questions with the full solution shown, so you can see
how the method is applied before you attempt the timed set.
Question 1
Which of the outlines A, B and C enclose the dot?
AA and C
BA, B and C
CB and C
DA and B
Answer: Option D — with explanation
Follow each outline round the dot in turn. The dot is inside A and B and outside the other outline.\nAn outline the dot is not inside is one the dot can be seen to be on the far side of, so no line has to be measured.
Common mistakes
- the dot is not inside exactly these outlines: A and C
- the dot is not inside exactly these outlines: A, B and C
- the dot is not inside exactly these outlines: B and C
Question 2
Which of the outlines A, B and C enclose the dot?
AA and C
BB and C
CA, B and C
DA and B
Answer: Option B — with explanation
Follow each outline round the dot in turn. The dot is inside B and C and outside the other outline.\nAn outline the dot is not inside is one the dot can be seen to be on the far side of, so no line has to be measured.
Common mistakes
- the dot is not inside exactly these outlines: A and B
- the dot is not inside exactly these outlines: A, B and C
- the dot is not inside exactly these outlines: A and C
Question 3
The outlines in the figure are labelled A, B and C. The dot lies inside which of them?
AB and C
BA and B
CA and C
DA, B and C
Answer: Option C — with explanation
Follow each outline round the dot in turn. The dot is inside A and C and outside the other outline.\nAn outline the dot is not inside is one the dot can be seen to be on the far side of, so no line has to be measured.
Common mistakes
- the dot is not inside exactly these outlines: B and C
- the dot is not inside exactly these outlines: A, B and C
- the dot is not inside exactly these outlines: A and B
Question 4
The outlines in the figure are labelled A, B and C. The dot lies inside which of them?
AA and B
BA and C
CB and C
DA, B and C
Answer: Option B — with explanation
Follow each outline round the dot in turn. The dot is inside A and C and outside the other outline.\nAn outline the dot is not inside is one the dot can be seen to be on the far side of, so no line has to be measured.
Common mistakes
- the dot is not inside exactly these outlines: B and C
- the dot is not inside exactly these outlines: A and B
- the dot is not inside exactly these outlines: A, B and C
Question 5
The outlines in the figure are labelled A, B and C. The dot lies inside which of them?
AA and C
BA, B and C
CB and C
DA and B
Answer: Option A — with explanation
Follow each outline round the dot in turn. The dot is inside A and C and outside the other outline.\nAn outline the dot is not inside is one the dot can be seen to be on the far side of, so no line has to be measured.
Common mistakes
- the dot is not inside exactly these outlines: A, B and C
- the dot is not inside exactly these outlines: B and C
- the dot is not inside exactly these outlines: A and B
Frequently asked questions
Do I need to measure anything?
No. The dot is placed so that it is plainly inside some outlines and plainly outside the others, well clear of every line. The answer can be seen by following the lines, not by measuring.
What if the dot looks as though it is on a line?
In a well-set figure it never is. A dot sitting on a line would have no answer, so the dot is always placed clear of every outline and the question is decided by the side it falls on.
How many outlines can there be?
Usually three. Two is too easy because there are only four combinations, and four makes the figure so busy that reading it becomes a test of eyesight rather than of reasoning.
Should I start with the largest outline?
Start with whichever you find easiest to follow, which is usually the outermost one. Settling one outline removes options straight away, and the rest of the figure then has less to hold in mind.
Take the Dot Situation test
Two timed papers on the same syllabus — sit the foundation paper first,
then the advanced one. Both use the real exam paper format with a full
step-by-step review of every question once you submit.
