On a particularly vain morning, Miss Loi was suddenly troubled by the perennial question: “Do sexy maths tutors actually exist?”
Similar feelings had surfaced in the past, and being a woman of action, she decided to settle this issue once and for all. So, to her feet she sprang and out (from an overworked photocopier) came a huge stack of leaflets containing the following multiple-choice question:
Do you think sexy maths tutors exist? Please tick ONE.
[ ] Holy Moly! You kidding me?! Yes of course!!!
[ ] No, don’t think so. Sorry, but I’m late for my optician appointment!
After some jostling with the promoters from various insurance, timeshare and credit card companies, Miss Loi managed to secure a prime spot at a busy Orchard Road junction to conduct her little survey for the good of mankind … but things didn’t go as smoothly as planned.
Many replied with a terse “Sorry already bought insurance!” when approached by her. Also, a certain k number of surveyees didn’t follow instructions and ended up ticking both boxes – it had to be said that many of these ‘culprits’ were in close attendance by their wives/girlfriends throughout the survey.
But worst of all, tragedy struck in the form of a strong gust of wind which scattered all her leaflets across Orchard Road just as she was packing up!
So …
The Venn diagram was drawn to represent the sets:
ε = {all those who were approached}
Y = {those who answered Yes}
N = {those who answered No}
Miss Loi managed to recall that:
n(Y ∩ N) = k,
n(Y) = 7 x n(Y ∩ N),
n(N) = 4 x n(Y ∩ N),
n(ε) = 6 x n(Y’ ∩ N’)
- Please help Miss Loi by first inserting, within the Venn diagram above, in each of its four regions, the number of people, in terms of k, represented by that region.
Being an extremely petty personBy a stroke of luck, Miss Loi actually kept count of a total of 165 persons who spurned her approach and did not answer the survey.Calculate the total number of persons approached by her. Hence state how many of those surveyed firmly (i.e. confirm chop stamp) believe in the existence of sexy maths tutors.
This being the swansong year for Sets & Venn Diagrams in A-Maths, there’s a niggling suspicion that it’s one of those chapters that will go out with a ‘bang’ i.e. last chance for examiners to set something sinister.
To excel in the land of the Sets, most of the time you’ll have to know some of their basic local language:
, φ, {}: Null or empty set- ∩: Intersect
- ∪: Union
- ⊆: Subset of
- ⊇: Superset of
- ∈: Element of
- n(P): number of elements in P
And be familiar with their diagrams:
Intersection:
Union:
WARNING: While most students should be able to answer 75% of this question, there’s a rare O-Level twister in its remaining portion which you’ll either get it very quickly or you won’t. So if this appears in the exam, please move on to the next question if you find that you’re more or less stuck.
Your grades are more important than the existence of sexy tutors!
