Onto the first question I looked at:
11. In the following expression 'box' is to be replaced with either + or - in such a way that the result of the calculation is 100.
123 'box' 45 'box' 67 'box' 89
The number of + signs used is p and the number of - signs is m. What is the value of p - m ?
A) -3 B) -1 C) 0 D) 1 E) 3
The solution given involved a nice bit of algebra using simultaneous equations but I wanted to develop a different method of act. So I looked at the possible solutions of p - m.
So if
- p = 3 and m = 0 then p - m = 3
- p = 2 and m = 1 then p - m = 1
- p = 1 and m = 2 then p - m = -1
- p = 0 and m = 3 then p - m = -3
So only these values need to be considered.
- If p - m = 3 . This is impossible since adding all the numbers won't result in the required number of 100.
- If p - m = -3. This is also impossible since subtracting the other three numbers from 123 won't result in 100.
- If p - m = 1. For this to occur we would have to add two of the numbers to 123 and subtract the remaining one. This is clearly impossible.
- This only leaves the case p - m = -1. Where we add one of the numbers and subtract the remaining two others.
Note To get this solution to the question I haven't had to do any hard calculations since I have just compared the size of the numbers present. I also haven't actually found out which numbers need to be added or subtracted. However I have answered the question.
Question Can I alter this question to make my method too hard to do so that the question ensures that the numbers needed to be added or subtracted have to be identified?
