June 2007 - Sec 1 - Game 1 - Q1

Moving to question one: If the last digit of an acceptable product code is 1, it must

be true that . . .

Alright so let's draw out a hypothetical for question one here. What it says is that the

last digit of an acceptable product code is 1. Well if the last digit is 1, we know for

certain that we are going to be in scenario two because 1 in scenario one is appearing

first.

So since we're in scenario two we know that 2 is going to be first; 4 is going to be second

because it's exactly twice the first value, or the first digit. Now what do we have left?

We have 0 and 3. We know that the third digit must less than the fifth digit, which means

0 must third, leaving 3 for four. So which one of the following must be true

(A), the first digit is 2. And you notice that must be true so (A) would be the correct

answer.

But again just going through the rest of these really quickly just to show you . . .

(B), the second digit is 0. No, in this case it is 4 and if it must be true it's always

the case. So one counter example would eliminate B.

(C), the third digit is 3. Again, the only possibility is that the third digit is

0 so C is out.

(D), the fourth digit is 4. Again, the fourth digit is 3 so D does not follow.

(E), the fourth digit is 0. Again, we know that the fourth digit is 3. So (A) would

be the correct answer.