Data Sufficiency

BTGModeratorVI wrote: ↑

Tue Mar 31, 2020 5:06 am

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.

Answer: A
Source: Official guide

For the hundreds digit of x to be equal to the sum of the hundreds digits of y and z, we must NOT have any carry from the sum for tens digits of y and z. This is what Statement 1 says. Sufficient.

Statement 2 is not sufficient since we do not know whether the sum for tens digits of y and z is equal to the tens digit of x. Insufficient.

The correct answer: A

Hope this helps!

-Jay
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BTGModeratorVI wrote: ↑

Tue Mar 31, 2020 5:06 am

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.

Answer: A
Source: Official guide

Target question: Is the hundreds digit of x equal to the sum of the hundreds digits of y and z ?

Notice that there are essentially 3 ways for the hundreds digit of x to be different from the sum of the hundreds digits of y and z
Scenario #1: the hundreds digits of y and z add to more than 9. For example, 600 + 900 = 1500. HOWEVER, we can rule out this scenario because we're told that x, y, and z are three-digit integers
Scenario #2: the tens digits of y and z add to more than 9. For example, 141 + 172 = 313.
Scenario #3: the tens digits of y and z add to 9, AND the units digits of y and z add to more than 9. For example, 149 + 159 = 308

Statement 1: The tens digit of x is equal to the sum of the tens digits of y and z.
This rules out scenarios 2 and 3 (plus we already ruled out scenario 1).
So, it must be the case that the hundreds digit of x equals to the sum of the hundreds digits of y and z
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The units digit of x is equal to the sum of the units digits of y and z.
This rules out scenario 3, but not scenario 2. Consider these two conflicting cases:
Case a: y = 100, z = 100 and x = 200, in which case the hundreds digit of x equals the sum of the hundreds digits of y and z
Case b: y = 160, z = 160 and x = 320, in which case the hundreds digit of x does not equal the sum of the hundreds digits of y and z
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent

BTGModeratorVI wrote: ↑

Tue Mar 31, 2020 5:06 am

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.

Answer: A
Source: Official guide

Solution:

Question Stem Analysis:

We need to determine whether the hundreds digit of x is equal to the sum of the hundreds digits of y and z, given that x, y, and z are three-digit positive integers such that x = y + z. Notice that this only can be the case if there is no “carryover” to the hundreds digit when we add the tens digits of y and z.

Statement One Alone:

This means there is no “carryover” to the hundreds digit when we add the tens digits of y and z. Furthermore, it means there is no “carryover” to the tens digit when we add the units digits of y and z (otherwise, the tens digit of x will not be equal to the sum of the tens digits of y and z). Statement one alone is sufficient.

Statement Two Alone:

This means there is no “carryover” to the tens digit when we add the units digits of y and z. However, it doesn’t mean there is no “carryover” to the hundreds digit when we add the tens digits of y and z. For example, if y = 123 and z = 234, then y + z = 123 + 234 = 357 = x. In this case, we see that the hundreds digit of x is the sum of the hundreds digits of y and z. However, if y = 153 and z = 264, then y + z = 153 + 264 = 417 = x. In this case, we see that the hundreds digit of x is not the sum of the hundreds digits of y and z because there is a “carryover” to the hundreds digit when we add the tens digits of y and z.

Answer: A