11)

Answer: C

12)

Answer: D

13)

Since triangles RYM and QMX are similar, the following is true:

Answer: E

14)

Answer: A

15)

Therefore there is no integer answer for b.

Answer: A

16)

According to the two rules the following is true

. All of the values described by this can be achieved

Answer: B

17)

So the solutions are the four roots of –1

Answer C

18)

The line through S and N is then If then

Answer: E

19)

Subtracting these two equations yields:

This implies that is divisible by 19 which is impossible if all possible m and n are positive integers less than 10.

Answer: A

20. Condition (i) tells us that we have to use each of 1, -1, i and -i the same number of times. Condition (ii) tells us that the sum must remain between zero and 2, so that we must arrange the numbers in such a way as to keep the sum in this interval. Condition (iii) says that the sum will not equal zero unless we are adding a multiple of 4 terms at a time. Clearly we can add , no n could be 1. Similarly, we could add

and all of the conditions are meet. However, when we try to add 12 terms (n = 3), there will only be 9 distinct sums, but there are 11 slots to fill before the final sum, so zero must occur once before getting to the last term.