## Tuesday, 11 October 2011

### Mistakes in Olympiad Maths Trainer 6 Book

This is posted by Lim Li ☺☻ My mother bought this book from Popular Bookstore for me to practise last year. I found many mistakes. Now that I am so free (PSLE is over!), I will type out some of the mistakes. My comments are in Red.

Week 2 Qn 5.
(a) Choose any three letters from a, b, c and d. In how many ways can we arrange these letters?
(b) A teacher wants to choose a captain and a vice-captain among 12 volleyball players. In how many ways can he do so?
Answer: (a) 4A3 = 4 x 3 x 2 = 24
(b)12C2 = (12 x 11 )/(2 x 1 ) = 66
(a) Should be 4P3
(b) Captain and vice-captain is different person, should be 12P2

Week 5 Qn 2. In a mathematics quiz, Fredric answered 1/9 of the questions wrongly. Paul answered 7 questions correctly. The number of questions that both of them answered correctly was 1/6 of the total number of questions. How many questions were there in the quiz?
First of all, from the 3rd statement, 1/6 of the total number of questions, one would naturally assume that it is the total number of questions in the mathematics quiz rather than the total number of questions both answered together, which is twice the amount. We also have to assume that all questions are answered correctly or wrongly. Logical interpretation of the question would lead to 36 as the answer.

Week 5 Qn 5. In the figure below, how many triangles can be formed using any three points as the vertice?
. . .
. . .
. . .
The correct solution is 9C3=84, 84-8=76 Answer: 76
Week 6 Qn 3: For 1^2 + 2^2 + 3^2 + ... + n^2, we can compute n(n + 1) (n + 2) /6. Find the value of 1^2 + 2^2 + 3^2 + ... + 15.^2
The formula in the question is wrong. It should be n (n + 1) (2n + 1) /6
Week 7 Qn 1. Don and Andy have some marbles. If Don gives some marbles to Andy, the number of marbles that Don has is twice the number of marbles what Andy has. If Andy gives the same number of marbles to Don, the number of marbles that Don has is 4 times of what Andy has. How many marbles does each of them have at first?
If the question does not provide any number, how are we supposed to find the number of marbles each of them has? I think the question should be: "What is the least possible number of marbles each of them has at first?"
Week 10 Qn 6. An athlete ran up the staircase of a building as part of his training programme. If he ran up the building at first and then walked up the last 24 steps, it would take him 28 seconds. If he ran up the building at first and then walked the last 36 steps, it would take him 30 seconds. How many steps were there on the staircases?
It is an impossible question, which cannot be solved. Too little information is given. Assuming speed is integer, there will be 3 solutions, 72, 288, 720 steps. If speed is not integer, the number of steps can be any integer above something, 36 I think. Anyway, if you see the solution given, the first statement totally didn't make any sense, and the 2nd statement is even worse.

Other questions with mistakes that I am too lazy to type. Sorry, only people who have purchased the book will understand what I am typing.