On the problem below OG 13th has a long explanation that I'm having a tough time to understand and i think is too complicated therefore time consuming on test day. Is there an easiest way to resolve this...
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 equal to the sum of the tens digits of y and z
2) The unit digit of x is equal to the sum of the units of y and z
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x = A B C
y = D E F
z = G H I
x = y + z
TO find: A = D + G
Statement 1:
B = E + F
This means that the Tens digits of y & z are between 0 & 4, inclusive. If the Digits are above that then the condition is voilated.
For example:
_ 4 _ + _ 3 _ ==> _ 7 _ YES
_ 6 _ + _ 5 _ ==> _ 1 _ NO
So, there will not be any carry forward for HUNDRED's digit.. So, x's Hundreds digit must be sum of y's & z's
SUFFICIENT
Statement 2:
We are given information about UNIT digit.. but we have no info for TENS,, maybe TENs digit has a carry forward for HUNDREDs or maybe not.
INSUFFICIENT
Answer [spoiler]{A}[/spoiler]
y = D E F
z = G H I
x = y + z
TO find: A = D + G
Statement 1:
B = E + F
This means that the Tens digits of y & z are between 0 & 4, inclusive. If the Digits are above that then the condition is voilated.
For example:
_ 4 _ + _ 3 _ ==> _ 7 _ YES
_ 6 _ + _ 5 _ ==> _ 1 _ NO
So, there will not be any carry forward for HUNDRED's digit.. So, x's Hundreds digit must be sum of y's & z's
SUFFICIENT
Statement 2:
We are given information about UNIT digit.. but we have no info for TENS,, maybe TENs digit has a carry forward for HUNDREDs or maybe not.
INSUFFICIENT
Answer [spoiler]{A}[/spoiler]
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Target question: Is the hundreds digit of x equal to the sum of the hundreds digits of y and z ?Maritadelcarmen 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 equal to the sum of the tens digits of y and z
2) The unit digit of x is equal to the sum of the units 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