Question 1027027: In the following problems, each group of lettered statements includes EXACTLY ONE false statement, and the rest are true.
I am thinking of a number. Which one of these statements is false?
A. The last digit is 1.
B. The number is divisible by 3.
C. The sum of its digits is 6.
D. The number is prime.
Answer by richard1234(7193)   (Show Source):
You can put this solution on YOUR website! If A is false, then B, C, and D are true. However no such positive integer exists, because if the digit sum is 6, then the integer is a multiple of 3 greater than 3 and cannot be prime.
If B is false, then C is false, a contradiction.
If C is false and the rest are true, then the number is a prime multiple of 3 whose last digit is 1. Only 3 could possibly work, but its last digit is not 1, so this case is out.
This only leaves D. If D is false and the rest are true, we can find an integer that works (e.g. 51, 411, 141, etc. but this is irrelevant). So D is false.
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