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.
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.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3
