Answer
The twin who lies is talking.
Work Step by Step
The given 2 statements form 2 equations.
Let the lucky number pair be x, y.
Statement 1: When I multiply my first lucky number by 3 and my second lucky number by 6,the addition of the resulting numbers produces a sum of 12:
\[3x+6y=12\](I)
Statement 2: When I add my first lucky number and twice my second lucky number, the sum is 5:
\[x+2y=5\](II)
Rewriting the equation(I) by taking out 3 factors:
\[x+2y=6\]
For any pair of numbers, only one equation can be true.
Hence, the twin who lies is talking.
