Comments on: Venn Diagrams To Prove The Existence of Sexy Tutors? http://www.exampaper.com.sg/questions/a-maths/venn-diagrams-to-prove-the-existence-of-sexy-tutors Sassy O Level Maths Tuition, Questions & Tips from Singapore's Favourite Private Tutor Sun, 05 Feb 2012 17:08:39 +0000 hourly 1 By: Mgccl http://www.exampaper.com.sg/questions/a-maths/venn-diagrams-to-prove-the-existence-of-sexy-tutors#comment-1477 Mgccl Sun, 14 Oct 2007 16:05:04 +0000 http://www.exampaper.com.sg/questions/a-maths/venn-diagrams-to-prove-the-existence-of-sexy-tutors#comment-1477 I don't know about it.. xD I'm in US... so I don't take the O-Level math. I don't know about it.. xD
I'm in US... so I don't take the O-Level math.

]]> By: Miss Loi http://www.exampaper.com.sg/questions/a-maths/venn-diagrams-to-prove-the-existence-of-sexy-tutors#comment-1472 Miss Loi Sun, 14 Oct 2007 03:22:33 +0000 http://www.exampaper.com.sg/questions/a-maths/venn-diagrams-to-prove-the-existence-of-sexy-tutors#comment-1472 Nice work Mgccl! Your workings are marked and some explanations added for the benefit of others. BTW Miss Loi suspects you're a little over-aged for O-Level maths no? Nice work Mgccl! Your workings are marked and some explanations added for the benefit of others.

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

]]> By: Mgccl http://www.exampaper.com.sg/questions/a-maths/venn-diagrams-to-prove-the-existence-of-sexy-tutors#comment-1471 Mgccl Sat, 13 Oct 2007 17:03:13 +0000 http://www.exampaper.com.sg/questions/a-maths/venn-diagrams-to-prove-the-existence-of-sexy-tutors#comment-1471 xD that's what I did wrong. yeah.. it's still possible to fill up everything.. <div class="highlight"> Miss Loi shall put up this diagram with the answers for easier reading and understanding: <img src="http://www.exampaper.com.sg/blog/wp-content/uploads/2007/10/venn-answer.gif" alt="Venn Diagram Answer" /> </div> n(Y∩N) = k <span class="highlight">Given</span> n(Y) = 7k <span class="highlight">= 7 x n(Y ∩ N) = 7k (Given)</span> n(Y∩N’) = n(Y) - n(Y∩N) = 6k <span class="highlight">Refer to the diagram if unsure</span> n(N) = 4k <span class="highlight">= 4 x n(Y ∩ N) = 4k (Given)</span> n(N∩Y’) = n(N) - n(Y∩N) = 3k <span class="highlight">Again refer to the diagram if unsure</span> <span class="highlight">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.</span> n(ε) is tougher n(ε) - n(Y’ ∩ N’) = n(Y∪N) <strong class="highlight">suppose n(Y’ ∩ N’) = x</strong>, we have <span class="highlight">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 <var>x</var>!</span> 6x - x = n(N∩Y’) + n(Y∩N’) + n(Y∩N) <div class="highlight"> 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 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. </div> 5x = 10 k x = 2k n(ε) = 12k n(Y’ ∩ N’) = 2k <span class="highlight">(which is also equivalent to the 165 pax who didn't answer the survey!)</span> <div class="highlight"> 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 <var>k</var> has a decimal point, <del>that's because Miss Loi had made a typo - she actually meant 166 pax</del> 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 ;) </div> xD that's what I did wrong.
yeah.. it's still possible to fill up everything..

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

Venn Diagram Answer

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

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 ;)

]]> By: Miss Loi http://www.exampaper.com.sg/questions/a-maths/venn-diagrams-to-prove-the-existence-of-sexy-tutors#comment-1470 Miss Loi Sat, 13 Oct 2007 16:44:46 +0000 http://www.exampaper.com.sg/questions/a-maths/venn-diagrams-to-prove-the-existence-of-sexy-tutors#comment-1470 Mgccl, 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 <em>confirm chop stamp</em> 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? Mgccl,

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?

]]> By: Peter http://www.exampaper.com.sg/questions/a-maths/venn-diagrams-to-prove-the-existence-of-sexy-tutors#comment-1469 Peter Sat, 13 Oct 2007 16:23:23 +0000 http://www.exampaper.com.sg/questions/a-maths/venn-diagrams-to-prove-the-existence-of-sexy-tutors#comment-1469 Mgccl - don't read too much into my comments... missloi doesn't :) Mgccl - don't read too much into my comments... missloi doesn't :)

]]> By: Mgccl http://www.exampaper.com.sg/questions/a-maths/venn-diagrams-to-prove-the-existence-of-sexy-tutors#comment-1468 Mgccl Sat, 13 Oct 2007 15:51:23 +0000 http://www.exampaper.com.sg/questions/a-maths/venn-diagrams-to-prove-the-existence-of-sexy-tutors#comment-1468 <b>Peter</b>: "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:
"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

]]> By: Miss Loi http://www.exampaper.com.sg/questions/a-maths/venn-diagrams-to-prove-the-existence-of-sexy-tutors#comment-1465 Miss Loi Sat, 13 Oct 2007 14:24:14 +0000 http://www.exampaper.com.sg/questions/a-maths/venn-diagrams-to-prove-the-existence-of-sexy-tutors#comment-1465 <strong>crazyhamster:</strong> Hamster rocks too. Especially your <a rel="external nofollow" href="http://crazyhamster.net/?p=64#comments" rel="nofollow">war report</a> lol <strong>Peter:</strong> In that case, don't be so gullible can? :D crazyhamster: Hamster rocks too. Especially your war report lol

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

]]> By: Peter http://www.exampaper.com.sg/questions/a-maths/venn-diagrams-to-prove-the-existence-of-sexy-tutors#comment-1459 Peter Sat, 13 Oct 2007 07:26:59 +0000 http://www.exampaper.com.sg/questions/a-maths/venn-diagrams-to-prove-the-existence-of-sexy-tutors#comment-1459 Because I'm gullible, missloi... :) You say you're a sexy maths 'cher, so I believe you. And, since you exist, you're real! And, I've never MET you, remember? Because I'm gullible, missloi... :) You say you're a sexy maths 'cher, so I believe you. And, since you exist, you're real!

And, I've never MET you, remember?

]]> By: crazyhamster http://www.exampaper.com.sg/questions/a-maths/venn-diagrams-to-prove-the-existence-of-sexy-tutors#comment-1456 crazyhamster Sat, 13 Oct 2007 05:04:59 +0000 http://www.exampaper.com.sg/questions/a-maths/venn-diagrams-to-prove-the-existence-of-sexy-tutors#comment-1456 what the! haha you rock man, can spin off a problem from this topic.... what the! haha you rock man, can spin off a problem from this topic....

]]> By: Miss Loi http://www.exampaper.com.sg/questions/a-maths/venn-diagrams-to-prove-the-existence-of-sexy-tutors#comment-1452 Miss Loi Sat, 13 Oct 2007 03:59:56 +0000 http://www.exampaper.com.sg/questions/a-maths/venn-diagrams-to-prove-the-existence-of-sexy-tutors#comment-1452 <b>Peter:</b> How do you <i>confirm chop stamp</i> know they exist when you haven't met any? Were you at Orchard Road the other day? :) <b>Mgccl: </b> Which brings us to the next hypothesis: The Existence of Sexy Maths Tutors that CAN teach calculus well. <b>Kiroii</b>: 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! Peter: How do you confirm chop stamp know they exist when you haven't met any? Were you at Orchard Road the other day? :)

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!

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