If x, y, and z are three-digit

Adam

Okay, so let's pretend that x = 300, y = 200 and z = 100. In this case, clearly, the hundreds digit of x is equal to the sum of the hundreds digits of y and z. So when is the initial prompt false?

Well, if the sum of the tens digits of y and z is 10 or more, then the 1 will carry to the hundreds place. In other words, if x = 300, y = 160 and z = 140, then the hundreds digit of x is not equal to the sum of the hundreds digit of y and z.

But note that, in this example, the sum of the tens digits of y and z is also not equal to the tens digit of x. Indeed, in order to carry over a 1 from the tens place to the hundreds place, the sum of the tens place of y and z must be 10 or more. But if this is true, then the sum of the tens digits of x and y cannot be equal to the sum of the tens digit of x, because the tens digit of x must be less than 10 (since it is just one digit).

So, in order for the sum of the hundreds digits of y and z to be different from the hundreds digit of z, the sum of the tens digits of y and z must be greater than 10. Statement 1 eliminates this possibility, and is thus sufficient.

Sep 24, 2019 • Reply