stunn3r
If a, b, and c are 3-digit positive integers, where a=b+c, is the hundreds' digit of a equal to the hundreds' digit of b plus the hundreds' digit of c?
(1) The tens' digit of a is equal to the tens digit of b plus the tens' digit of c.
(2) The units' digit of a is equal to the units' digit of b plus the units' digit of c.
What is the source of this question?
The sum of the hundred's digits of a & b will equal the hundred's digit of c if nothing "carries" from the tens column.
123 + 351 = 474
123 + 358 = 481
Both of those lead to "yes" answer to the prompt question.
In order for statement #1 to be true, it must be true that nothing carries from the ones column to the tens column (only the first of the two example addition statements satisfies this) --- thus, statement #1 automatically implies statement #2. That's why statement #1, by itself, is sufficient --- it already completely contains the information in statement #2. That's why
(A) has to be the answer.
In other words, I am claiming that it is utterly impossible to find numbers that satisfy both the prompt condition and statement #1 but not statement #2. In order for
(C) to be the answer, there would have to be a case in which you could add two three digit numbers which met statement #1, did not meet statement #2, and the three-digit sum did not work out neatly in the hundreds column. You would have to able to find such a case, and I claim that finding such a case is impossible. That's why
(C) can't be the answer.
Does all this make sense?
Mike