2001 IMC solutions
1 A
2 E
3 A
4 E
5 C
6 D
7 C
8 A
9 D
10 B
11 B
12 E
13 B
14 C
15 C
16 B
17 C
18 E
19 E
20 D
21 A
22 C
23 D
24 D
25 D
Hints:
4. Don't forget to count her direct descendants and their children.
15. Square all the numbers and compare with 100.
16. If x is the number of cakes and y is the number of buns, we have to find x such that 512-39*x is divisible by 23 (or y such that 512-23*y is divisible by 39)
17. For each minute of "real time" the clocks show different times for 20 seconds. So they agree 2/3rd of the time
19. If width is w and height is h, the diagram gives 4w=5h. Rearranging 9*(4/5)*x^2 is the total area. So check 5/36*options for a perfect square.
23. (n+3)/(n-1) = 1 + 4/(n-1)
24. Top row adds to 30, the diagonal with slope +1 adds to 39. So the columns and diagonals must add to give 30 to 39 inclusive.
25. The arc centre B (or A) has radius sqrt(2), with subtended angle 90 degrees.