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If x, y, and z are three-digit positive integers and if x = [#permalink]
 18 Sep 2012, 09:10
Question Stats:
50% (02:03) correct
49% (01:13) wrong based on 73 sessions
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?? _________________
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Last edited by Bunuel on 18 Sep 2012, 09:16, edited 1 time in total.
Renamed the topic and edited the question.
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Re: If x, y, and z are three-digit positive integers and if x = [#permalink]
18 Sep 2012, 11:04
conty911 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 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?? 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"
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Re: If x, y, and z are three-digit positive integers and if x = [#permalink]
18 Sep 2012, 11:06
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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
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Re: If x, y, and z are three-digit positive integers and if x = [#permalink]
18 Sep 2012, 21:13
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.
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Re: If x, y, and z are three-digit positive integers and if x = [#permalink]
20 Sep 2012, 00:12
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
Last edited by mbaiseasy on 15 Jan 2013, 01:23, edited 1 time in total.
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Re: If x, y, and z are three-digit positive integers and if x = [#permalink]
14 Jan 2013, 02:52
abhishekkpv wrote: 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 so this is sort of a number property?
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Re: If x, y, and z are three-digit positive integers and if x = [#permalink]
23 Feb 2013, 03:18
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.
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Re: If x, y, and z are three-digit positive integers and if x = [#permalink]
13 Apr 2013, 11:23
abhishekkpv wrote: 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 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
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Re: If x, y, and z are three-digit positive integers and if x = [#permalink]
13 Apr 2013, 11:27
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mokura wrote: 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!
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Re: If x, y, and z are three-digit positive integers and if x = [#permalink]
13 Apr 2013, 11:29
Zarrolou wrote: mokura wrote: 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! ouffff thanks so much for the quick reply and clarification. should re-read the question next time
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Re: If x, y, and z are three-digit positive integers and if x =
[#permalink]
13 Apr 2013, 11:29
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