# June 2007 - Sec 1 - Game 1 - Q1

## Video Transcript:

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Moving to question one: If the last digit of an acceptable product code is 1, it must
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be true that . . .
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Alright so let's draw out a hypothetical for question one here. What it says is that the
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last digit of an acceptable product code is 1. Well if the last digit is 1, we know for
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certain that we are going to be in scenario two because 1 in scenario one is appearing
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first.
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So since we're in scenario two we know that 2 is going to be first; 4 is going to be second
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because it's exactly twice the first value, or the first digit. Now what do we have left?
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We have 0 and 3. We know that the third digit must less than the fifth digit, which means
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0 must third, leaving 3 for four. So which one of the following must be true
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(A), the first digit is 2. And you notice that must be true so (A) would be the correct
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But again just going through the rest of these really quickly just to show you . . .
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(B), the second digit is 0. No, in this case it is 4 and if it must be true it's always
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the case. So one counter example would eliminate B.
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(C), the third digit is 3. Again, the only possibility is that the third digit is
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0 so C is out.
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(D), the fourth digit is 4. Again, the fourth digit is 3 so D does not follow.
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(E), the fourth digit is 0. Again, we know that the fourth digit is 3. So (A) would
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