If x, y, and z are three-digit positive integers and if x =

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 =

Cheers,
Brent

Question is demanding 100 digit of Y + 100 digit of Z is equal to 100 digit of X, means there will not be any carryover from the sum of tens digit of Y and Z. therefore from Option 1, sum of tens digit of Y and Z equal to of X means there will not be any carryforward from here to 100 digit of Y and Z. therefore option 1 is sufficient to answer.
Option 2 unit digit sum is equal, will not give any indication whether tens digit will not carryforward any to hundered. therefore this is not sufficient.

ANswer "A"

Let x= a b c
y = d e f
z= g h i

x= y+z

1 --> b= e+h which in turn implies c=f+i and so a=d+g (and this implies there is no carry forward in the addition of units and tens place digit of the two numbers)

2--> c=f+i which does not tell us if b= e+h(as there could be a carry forward bcos of this addition to the hundred place)

and so the answer is A

The concern here is the sum of the tenth digit might have a carryover, so the sum of the hundredth digit on Y & Z might not be equal to X's hundredth digit. So A is the right answer.

Let the 3 digit numbers be,
x=ABC
y=DEF
z=GHI

Now, its given that
DEF
+ GHI
_____
ABC
_____

Statement 1---- says that E+H=B. Substitute any digit for E and H, you will find that D+G must be equal to A. Sufficient
Statement2.......says F+I=C. E and H can be anything and in turn D and G can be anything. Not sufficient.

my confusion is the following regarding (1). maybe i am not reading the question right, but assume the following:

y: 6 4 3
z: 4 4 2

x: 1 0 8 5

so, the tens digit of x is equal to the sum of the tens digit of y + z. however, the hundreds digit, 6 + 4 = 1 0. The hundreds digit of x would be 0. can someone please explain? thank you

Your problem is very simple : "x, y, and z are three-digit positive integers".
x cannot be 1085, it must be \(\leq{999}\)

P.S: welcome to GmatClub!

For Statement I my problem pertains to the fact that the ten's digit of x will be expressed as ten's digit of y + ten's digit of z.
But if y=190 ,z=190 then x =380 the 1 does carry over from the ten's digit.
Although the ten's digit of x is the sum of ten's digit of y and z.

Please Elaborate

The tens digit of y is 9 and the tens digit of z is 9 --> 9+9=18 not 8.

Hope it's clear.

What about

882 = 541 + 341 tens digit satisfies but ans is not.. don't know where I am wrong

You are getting the same YES answer. The hundreds digit of x, which is 8 in your example, equals to the sum of the hundreds digits of y and z, which are 5 and 3: 5 + 3 = 8.

Bunuel, your explanations are top notch! Thank you so much!

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

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.
From this statement , we can conclude that there is no carry over from tens place to hundred place. That means hundreds digit of x equal to the sum of the hundreds digits of y and z . Hence Sufficient.

Example:

235
+452
-------
687
Here the tens digit of x is equal to the sum of the tens digits of y and z. ==> 3+5=8
That's why the hundreds digit of x equal to the sum of the hundreds digits of y and z ==>2+4=6

Another example:
295
+452
-------
747
Here the tens digit of x is not equal to the sum of the tens digits of y and z. ==> 9 + 5 ≠ 4
That means there is carry over of 1 from tens to hundreds place and that's why the hundreds digit of x will not be equal to the sum of the hundreds digits of y and z
2 + 4 ≠ 7

(2) The units digit of x is equal to the sum of the units digits of y and z.
From this statement we can conclude that there is no carry over from units place to tens place. But we are not sure whether there is a carry over from tens to hundreds place. Hence statement 2 is insufficient

Option A is the correct answer.

Thanks,
Clifin J Francis,
GMAT SME

Answer: Option A

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In this how you can take 2nd eg. according to statement 2
153
147
300

0 is not sum of 3+7

If this eg is correct then we can also take according to statement 1
153
156
309

Here hundreds digit of x is not equal to hundreds digit of x & y.

I am not completely satisfied with any of the explanations. Can someone please clear this?

Thanks.

I think you misunderstood the solution. (i) and (ii) are general examples, and not the cases for (1) and (2).