I'm in US... so I don't take the O-Level math. ]]>

BTW Miss Loi suspects you're a little over-aged for O-Level maths no?

]]>yeah.. it's still possible to fill up everything..

Miss Loi shall put up this diagram with the answers for easier reading and understanding:

n(Y∩N) = k Given

n(Y) = 7k = 7 x n(Y ∩ N) = 7k (Given)

n(Y∩N’) = n(Y) - n(Y∩N) = 6k Refer to the diagram if unsure

n(N) = 4k = 4 x n(Y ∩ N) = 4k (Given)

n(N∩Y’) = n(N) - n(Y∩N) = 3k Again refer to the diagram if unsure

Yes from what is given, students should not have any problems inserting the values in the first three regions. These are marks served on a platter.

n(ε) is tougher

n(ε) - n(Y’ ∩ N’) = n(Y∪N)

**suppose n(Y’ ∩ N’) = x**, we have

The only clue you're given with regards to the fourth region (i.e. n(Y’ ∩ N’)), is n(ε) = 6 x n(Y’ ∩ N’). So it's imperative that you recognize the first step is to let this 4th region be `x`!

6x - x = n(N∩Y’) + n(Y∩N’) + n(Y∩N)

So given that n(ε) = 6 x n(Y’ ∩ N’) = 6x, and entire region outside the two circles = x (as assigned by yourself),

⇒ entire region within the two circles = 6x - x = 5x

⇒ entire region within the two circles = 6x - x = 5x

From your earlier workings, the region within the two circles is also equivalent to 6k+k+3k = 10k

⇒ 5x = 10k

... rest of workings are as straightforward as you've shown.

5x = 10 k

x = 2k

n(ε) = 12k

n(Y’ ∩ N’) = 2k (which is also equivalent to the 165 pax who didn't answer the survey!)

This is the part that left many stumped. Some (like you obviously) get it quickly while others can get stuck here a long time. That's why Miss Loi advise to move on (and revisit the last part of this question later when you have the time) if you're stuck. Afterall you should've already scored a decent amount of marks from the first portions of this question.

As for why `k` has a decimal point, ~~that's because Miss Loi had made a typo - she actually meant 166 pax~~ let's just assume that some of the people she surveyed were deemed too under-aged to discern the meaning of 'sexiness' - so these kids only count as half-persons 😉

You are brilliant! Not all O-Level students can jump straight to Part 2 and solve the whole question via making use of the 165 persons who didn't participate.

Though your answer is not quite right in the end, you're forgiven coz you probably didn't understand the term *confirm chop stamp* which means "100% sure" in our local context - which means you should exclude those hesitant ones who answered both Yes and No, hence you should be looking for:

n(Y∩N’) = (825/10)*6 = 495

BUT students will typically attempt part 1 before even taking a glance at part 2. So if you don't know about the 165 pax in part 2, do you think you'd still be able to fill up the four regions in Part 1?

]]>"since you exist"

how do you know Miss Loi really exist?

From "I think therefore I am"? then substitute I with Miss Loi?

"I think therefore I am" Logically equal to "I don't think therefore I am not"

I love math jokes...

anyway.. I tried to solve the question.. and here is what I got in 30 seconds, and I guess I'm wrong:

because

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’)

suppose n(Y), n(N)

we have

n(Y) = 7k

n(N) = 4k

we know how many people didn't chose, 165

so we have

n(ε) = 165 * 6

and

n(ε) = 6* 165 = 990(yeeeah... ~~~)

n(Y ∪ N) = n(ε) - 165

= 825

now just have to find the value of k.

because we know. there exist a k in y and n, so subtract one from each of them.

we get

n(Y∩N') = 6k

n(N) = 4k

n(Y∩N') ∪ n(N) = n(Y ∪ N)

so 10k = 825

therefore

n(Y) = 825/10*7 = 577.5

because there is a decimal... so it don't seems like the right answer...

I failed!!! T.T

**Peter:** In that case, don't be so gullible can? 😀

And, I've never MET you, remember?

]]>**Mgccl: ** Which brings us to the next hypothesis: The Existence of Sexy Maths Tutors that CAN teach calculus well.

**Kiroii**: Surely you can easily do the first few parts of this question? As shown from past records, Miss Loi will only comment when someone has at least attempted the question here. Spoonfeeding is taboo in Jφss Sticks!