Posted by Graham on Monday, May 2, 2011 at 12:00pm.
You're looking for an integer (I assume) between 11 and 19 inclusive: that comes from the first statement. So try multiplying each of 11, 12, 13, 14, 15, 16, 17, 18 and 19 by 6, and look at the final digit. If it's an 8, that's a possible solution. Of the above, 13 is a possibility (6x3 ends in 8), and 18 is another possibility (8x6 ends in 8). Which of 13 and 18 when multiplied by 4 ends in a 2? Well, actually both of them do: 4x13=52, and 4x18=72. So I'd say that you've got two possible solutions. Have I made a mistake? Check it. If the answer is 13, multiply that by 2 and I get 26 which is between 22 and 38 inclusive; if I multiply 13 by 6 I get 78 which ends in an 8, and 13 times 4 is 52 which ends in 2. But if the answer is 18, then twice that is 36 which is also between 22 and 38 inclusive; if I multiply it by 6 I get 108 which ends in 8, and if I multiply it by 4 I get 72, which ends in 2. Are you sure you've got the question right?