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

Question

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.

Is it safe to conclude that the place value of an integer number (represented as a sum of different integers), depends upon only the preceding place value of integers being summed up?

for eg:
x=1000a+100b+10c+1d
y=1000e+100f+10g+1h
z=1000l+100m+10n+1p
if z=x+y then

is l only dependent upon value of b and f or some other parameters also??

Bunuel · Accepted Answer

The question basically asks whether there is a carry over 1 from the tens place to the hundreds place.

Consider the following examples:
(i)
123
 234 
357

Here when we add the tens digits 2 and 3 there is no carry over 1 from the tens place to the hundreds place, thus the hundreds digit of x (3) is equal to the sum of the hundreds digits of y (1) and z (2).

(ii)
153
 147 
300

Here when we add the tens digits 5 and 4 and carry over 1 from the units place, we get 10, so we have carry over 1 from the tens place to the hundreds place, thus the hundreds digit of x (3) does NOT equal to the sum of the hundreds digits of y (1) and z (1).

The first statement implies that there is no carry over 1 from the tens place to the hundreds place, thus the hundreds digit of x is equal to the sum of the hundreds digits of y and z. Sufficient.

The second statement does not provide us with sufficient information about carry over 1 from the tens place to the hundreds place.

Answer: A.

Hope it's clear.

mbaiseasy · Answer

x = ABC
y = DEF
z = GHI

DEF
+GHI
_____
 ABC

Question: Is D + G = A? This is true if there is no carry-over from the tens digits' sum.

1. E + H = B, This means there is no carry over to hundreds position. SUFFICIENT.
2. C + F = I, This means there is no carry over to tens position BUT we do not know if there will be a carry over during the sum of tens. INSUFFICIENT.

Answer: A

BrentGMATPrepNow · Answer

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

jitgoel · Answer

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"

abhishekkpv · Answer

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

1022lapog · Answer

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.

rajathpanta · 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.

mokura · Answer

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

Zarrolou · Answer

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!

Abheek · Answer

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

Bunuel · Answer

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

Hope it's clear.

Cheryn · Answer

What about

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

Bunuel · Answer

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.

advait92 · Answer

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

ScottTargetTestPrep · Answer

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

CrackverbalGMAT · Answer

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

GMATinsight · Answer

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BansalT · Answer

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.

Bunuel · Answer

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

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

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

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