fozzzy wrote:
If x, y, and z are three-digit positive integers and if x = y + z, is the hundreds digit of x equal to the sum of the hundreds digits of y and z ?
(1) The tens digit of x is equal to the sum of the tens digits of y and z.
(2) The units digit of x is equal to the sum of the units digits of y and z.
Is there an alternative approach for this problem?
The question basically asks whether there is a carry over 1 from the tens place to the hundreds place.
Consider the following examples:
(i)
123
234357
Here when we add the tens digits 2 and 3 there is no carry over 1 from the tens place to the hundreds place, thus the hundreds digit of x (3) is equal to the sum of the hundreds digits of y (1) and z (2).
(ii)
153
147300
Here when we add the tens digits 5 and 4 and carry over 1 from the units place, we get 10, so we have carry over 1 from the tens place to the hundreds place, thus the hundreds digit of x (3) does NOT equal to the sum of the hundreds digits of y (1) and z (1).
The first statement implies that there is no carry over 1 from the tens place to the hundreds place, thus the hundreds digit of x is equal to the sum of the hundreds digits of y and z. Sufficient.
The second statement does not provide us with sufficient information about carry over 1 from the tens place to the hundreds place.
Answer: A.
Hope it's clear.
What if there is a carry over from ones digit to tens digit. The sum of y and z tens digit would still be the same(without carry over), but the carry over from one would add in the final sum, resulting in carry over to hundreds digit. this would make two scenarios for option a. this is the reason I crossed option A and went for option C. Please clarify!