Ridiculously tough Pr. Sch MAth Qns

Hi everybody. Recently I've been working at the World Book Fair'05 for the past week, under the company of Math Teach. This is a company with 30+ yrs of history tutoring maths, in a bungalow turned tuition center along Frankel Drive. (somewhere at Kembangan) For this book fair the director has came out with a series of Primary School Math Manuals, featuring challenging problem sums and very detailed worked solutions. My job is to promote this manuals to parents, educators and earn my commission. Quite a nice job, though my sales may not be fantastic.

I've browsed thru the manuals. They're indeed brilliant Mathematics guides for Pr Sch students, written from the author's 30+ yrs of experience in tutoring. For those with brothers & sisters studying Pr Sch and have problems with scoring can come down take a look b4 considering tuition. Its more worthwhile.

The promoters hired are mainly undergrads having holiday and unemployed like me. At work, the author like to flash Exam Qns brought in by parents on a projector screen. Some of these Qns were shockingly difficult, so much so that the undergrads in Engineering, Majors in Maths working with me also can't help scratching their heads. I hereby post 3 of the more difficult Qns to my friends out here, who might still have an interest in challenging math Qns.

Q1.
100 students sits in a circle. A teacher gave out sweets to alternate students, starting from student 1. She continue to give out the sweets until every student has a sweet. Which is the last student to get the sweet?

This Qn comes from Kwang Hua Pr. Sch, Pr4 streaming exam. The whole school only has 1 student got it right... and I suppose he did it by brute force calculations

I solved by multiples, but can't get the ans. My answer was 64. My friends wrote out the numbers, cancelled number by number and found the answer to be 72.

Q2.
There are 100 pple in a room. If each person shoke hands with all others in the room once, how many handshakes were there altogether?

This Qn came from another sch in the East, I think is Tao Nan Pr Sch. Less tough but damn ridiculous, using a JC Qn for their Pr Sch exams. Wonder what they're expecting from their students...

I was glad I was ythe fastest to solve it, even faster than the undergrads... yeah! I got the ans by finding the increment in handshakes from 2 pple to 5 pple, and then work out the number pattern. A better method I saw from an electrical engineer undergrad would be to use AP, GP formula... something I've forgotten after JC. The ans we got was 4950 handshakes.

Q3.
I have a nunber.
When I divide the number by 9, the remainder is 8.
When I divide the number by 8, the remainder is 7.
When I divide the number by 7, the remainder is 6.
When I divide the number by 6, the remainder is 5.
When I divide the number by 5, the remainder is 4.
When I divide the number by 4, the remainder is 3.
When I divide the number by 3, the remainder is 2.
When I divide the number by 2, the remainder is 1.
What is the smallest posssible number I have?

This is the most er xin Pr Sch exam Qn I've ever seen. If I took the exam I would just give up the 5 marks right away. This is an equivalent of Australian Maths competition at Sec Sch Level, how can a sch be so unkind to set it for kids <12>

10 out of 11 of the promoters had a min of GCE A' Levels certs. 7 are undergrads in fields like acc, EE and major in Maths. None got it right. Only an acc undergrad got close.She got a number that suits all the criteria but she did not get the smallest possible number. What she did was (5x6x7x8x9)-1 = 15119. Her approach was correct. I analysed the Qn at home. (2x3x4x5x6x7x8x9)-1 will gives an answer that satisfy the criterias but will not be the samllest possible number. 2,4 are factors of 8 so can be neglected. 3 is a factor of 9 so can be neglected. 6 can be split into its component factors 2 & 3, so 6 should be neglected as well since 2 & 3 are factors of 8 & 9 respectively. Hence ans: (5x7x8x9)-1 = 2519.

Arn't they difficult? My boss had the Qns posted out forPr Sch students to try. Prizes can be won if anyone got all 3 Qns answered correctly. I thought its crap. Amazingly, a Pr Sch guy did got all 3 Qns answered correctly. I din see him but I think he's a gifted progamme student or an Indian genius who came to the booth. Pr Sch man!!! What brand of milk his mother fed him.

After seeing these 3 Qns and many more other different Pr Sch Qns brought up by parents and students themselves, I really dunno what Pr Schools are becoming these days. Their kiasu-ness is really outrageous or are children getting cleverer... Makes me feel glad that PSLE was over for me and ponder over what my children will be studying in future...