If x, y, and z are three-digit positive integers and if x = y+z, is the hundreds digits 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 z is equal to the sum f the units digits of y and z.
Let y = 2BC, z = 2EF, and x = HTU, so that the addition looks as follows:
2BC
2EF
HTU
When will it be true that H ≠ 2+2?
When we have to CARRY A 1 FROM THE TENS PLACE TO THE HUNDREDS PLACE.
To illustrate:
259
249
508
Here, because we have to carry a 1 from the tens place to the hundreds place, H = 2+2+1 = 5.
Question rephrased:
ABC
DEF
HTU
In the addition problem above, do we have to a carry a 1 from the tens place to the hundreds place?
Statement 1: The tens digit of x is equal to the sum of the tens
digits of y and z.
Since T = B+E, there is no need to carry a 1 to the hundreds place.
SUFFICIENT.
Statement 2: The units digit of x is equal to the sum of the
units digits of y and z.
Since U = C+F, we do not need to carry a 1 from the UNITS PLACE to the TENS PLACE.
But it cannot be determined whether we have to carry a 1 from the TENS PLACE to the HUNDREDS PLACE.
If T = B+E = 0+0 = 0, then there is no need to carry a 1 to the hundreds place:
If T = B+E = 9+9 = 18, then we must carry a 1 to the hundreds place.
INSUFFICIENT.
The correct answer is
A.
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