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AB + CD = AAA, where AB and CD are twodigit numbers and AAA is a thre
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06 Aug 2012, 10:57
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AB + CD = AAA, where AB and CD are twodigit numbers and AAA is a three digit number; A, B, C, and D are distinct positive integers. In the addition problem above, what is the value of C? (A) 1 (B) 3 (C) 7 (D) 9 (E) Cannot be determined
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Re: AB + CD = AAA, where AB and CD are twodigit numbers and AAA is a thre
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06 Aug 2012, 11:06
navigator123 wrote: AB + CD = AAA, where AB and CD are twodigit numbers and AAA is a three digit number; A, B, C, and D are distinct positive integers. In the addition problem above, what is the value of C?
(A) 1 (B) 3 (C) 7 (D) 9 (E) Cannot be determined Since AB and CD are twodigit integers, their sum can give us only one three digit integer of a kind of AAA: 111. So, A=1 and we have 1B+CD=111 Now, C can not be less than 9, because no twodigit integer with first digit 1 (1B<20) can be added to twodigit integer less than 90, so that to have the sum 111 (if CD<90, so if C<9, CD+1B<111). Hence C=9. Answer: D.
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Re: AB + CD = AAA, where AB and CD are twodigit numbers and AAA is a thre
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16 Aug 2012, 11:11
Hi Bunuel, Doesn't 82+19=111. But you say no two digit number with 1st digit as 1 can be added to a number less than 90 to get a sum of 111. Can you elaborate?? One more thing is only 111 fits into this scenario as it is the sum of two digit numbers which cannot exceed 188 right??
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Re: AB + CD = AAA, where AB and CD are twodigit numbers and AAA is a thre
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17 Aug 2012, 22:10
Hi Bunuel
How did u check that there is only one such number as AAA when AB and CD are added together..Please can you explain the logic behind it?



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Re: AB + CD = AAA, where AB and CD are twodigit numbers and AAA is a thre
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25 Feb 2014, 20:43
AB+CD=AAA 10A+B+10C+D=100A+10A+A 10C+B+D=101A (10C+B+D)/101=A Just need to realize that A,B,C,D are integers that cannot exceed 9, as they are single digits Keeping this in mind, C is at most 9, so (90+B+D)/101=A >B+D=11 and A=1 For A = 2, it becomes obvious that either B, C, or D will have to exceed 9 and is thus not possible. So C=9
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Re: AB + CD = AAA, where AB and CD are twodigit numbers and AAA is a thre
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28 Mar 2014, 00:56
\(AB + CD = AAA\) We can write it down as : \(A(10) + B + C(10) + D = A(100) + A(10) + A\) \(B + D + C0 = A00 + A\) \(B + D + C0 = A0A\) C0 must be 90 else addition of two single digit B and D wont be able to form a triple digit number e.g if C0=80 then even 80+9+9 = 98. C = 9 Answer is D\(B + D + 90 = 101\) Note : further \(B + D = 11\) and \(A = 1\)
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Re: AB + CD = AAA, where AB and CD are twodigit numbers and AAA is a thre
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13 Jun 2015, 03:35
surendar26 wrote: AB + CD = AAA, where AB and CD are twodigit numbers and AAA is a three digit number; A, B, C, and D are distinct positive integers. In the addition problem above, what is the value of C?
(A) 1
(B) 3
(C) 7
(D) 9
(E) Cannot be determined Answer in Two stepsStep 1: AB + CD = AAA i.e. Sum of two 2digit numbers is a three digit number but sum of two 2digit number must be less than 200 hence the 3Digit number must have Hundreds digit as 1 i.e. A = 1 Step 2: If one 2Digit number is in 10s i.e. less than 20 (AB here as A=1) then other two digit number must be in either 80s or 90s in order to give the sum of two greater than 100 i.e. CD must have C either 8 or 9 only. [Since number D in CD is unknown so it gives us opportunity to make summation 111 anyways] Of 8 and 9, only 9 is the available option Answer: Option
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Re: AB + CD = AAA, where AB and CD are twodigit numbers and AAA is a thre
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15 Jun 2015, 05:46
Well the trick here is to actually realise that AAA emeans that this is the same three digits (in my mind this is not very clear). After you have this straight then even testing does not take long. E.G:
AB + CD = AAA, we can use these numbers for A,B,C,D: 1,2,3,4,5,6,7,8,9
1) Starting with adding the largest numbers possible: 67+89 = we get 156. So we know that the hindreds digit must be one, as we cannot have any larger hundreds digit.
2) This means that AAA = 111. So, A = 1
3) Now we need to surpass 10 in the addition of B and D and also get to 11.
4) Testing shows that 12+ 89 = 101, but 12+78 = 90. So, we should start trying with a combination of 2 low and 2 large numbers.
5) Trying the largest possible for B and D, 9+2 = 11. Visually we have this: 1___B __+__ C___D __=__ 111
Choose 2 for B and 9 for D (to reach 11) and you will see that it does not work because then you have already used 9 and the second largest number (8) is not enough to reach 11.
Trying the same with 3 for B and 8 for D, you reach 111.
This means that your addition in the end is: 13+98, so C is 9.



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Re: AB + CD = AAA, where AB and CD are twodigit numbers and AAA is a thre
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20 Jul 2017, 03:45
Please ignore
One thing i am clear that the no has to be 111. But why is 24+87=111 wrong?



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Re: AB + CD = AAA, where AB and CD are twodigit numbers and AAA is a thre
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Re: AB + CD = AAA, where AB and CD are twodigit numbers and AAA is a thre
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25 Nov 2017, 10:18
BunuelIs this a GMAT like question? What is the actual source of this question?



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Re: AB + CD = AAA, where AB and CD are twodigit numbers and AAA is a thre
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Re: AB + CD = AAA, where AB and CD are twodigit numbers and AAA is a thre
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10 Dec 2018, 05:31
navigator123 wrote: AB + CD = AAA, where AB and CD are twodigit numbers and AAA is a three digit number; A, B, C, and D are distinct positive integers. In the addition problem above, what is the value of C?
(A) 1 (B) 3 (C) 7 (D) 9 (E) Cannot be determined chetan2uPlease help. The question says that AAA is a 3digit number. Nowhere is it mentioned that AAA have the same digits. How it is possible to narrow down AAA to 111?



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Re: AB + CD = AAA, where AB and CD are twodigit numbers and AAA is a thre
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10 Dec 2018, 06:03
ParthSanghavi wrote: navigator123 wrote: AB + CD = AAA, where AB and CD are twodigit numbers and AAA is a three digit number; A, B, C, and D are distinct positive integers. In the addition problem above, what is the value of C?
(A) 1 (B) 3 (C) 7 (D) 9 (E) Cannot be determined chetan2uPlease help. The question says that AAA is a 3digit number. Nowhere is it mentioned that AAA have the same digits. How it is possible to narrow down AAA to 111? Hi.. If it's mentioned that AAA is a 3digit number and A is a distinct digit, this means that the 3 digits in AAA are all As.
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AB + CD = AAA, where AB and CD are twodigit numbers and AAA is a thre
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Updated on: 14 Feb 2019, 04:06
navigator123 wrote: AB + CD = AAA, where AB and CD are twodigit numbers and AAA is a three digit number; A, B, C, and D are distinct positive integers. In the addition problem above, what is the value of C?
(A) 1 (B) 3 (C) 7 (D) 9 (E) Cannot be determined A really interesting question, Even we can make 4 cases such as AB 1D AB 3D AB 7D AB 9DIf we look at case 4, only this can satisfy our condition, A, B, C, and D are distinct positive integers _16 +95 111
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AB + CD = AAA, where AB and CD are twodigit numbers and AAA is a thre
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14 Feb 2019, 04:03
I think, I can suggest one more way to tackle this problem. AAA = AB + CD, which implies below: AAA  AB =CD i.e. 3 digit number  2 digit number to give 2 digit number. Hence A<B, because tens digit of AAA and AB are same (if A>=B, we will get 3 digit number as the answer and not 2 digit, which is the case at hand). Therefore C has to be equal to 9. Also, AAA should be equal to 111 i.e. 1111B = 9D, where B>1.



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Re: AB + CD = AAA, where AB and CD are twodigit numbers and AAA is a thre
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14 Feb 2019, 13:02
navigator123 wrote: AB + CD = AAA, where AB and CD are twodigit numbers and AAA is a three digit number; A, B, C, and D are distinct positive integers. In the addition problem above, what is the value of C?
(A) 1 (B) 3 (C) 7 (D) 9 (E) Cannot be determined AB CD  AAA  look carefully at B+D: it gives 10 + A. So B+D=10 + A Now lets get into the calculation part: 10A + B +10C + D = 100A + 10A + A 10A + 10 + A + 10C = 111A 10 + 10 C = 100A 10(1+C) = 100A 1+ C = 10A It is given that a,b,c and d are single digit nos. So in order for that statement to hold true. The value of A can only be 1. So, 1 + c = 10 C= 9 .option D is the correct answer.
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Re: AB + CD = AAA, where AB and CD are twodigit numbers and AAA is a thre
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