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AB + CD = AAA, where AB and CD are two-digit numbers and AAA is a thre

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AB + CD = AAA, where AB and CD are two-digit numbers and AAA is a thre  [#permalink]

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New post 06 Aug 2012, 09:57
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AB + CD = AAA, where AB and CD are two-digit 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 two-digit numbers and AAA is a thre  [#permalink]

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New post 06 Aug 2012, 10:06
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navigator123 wrote:
AB + CD = AAA, where AB and CD are two-digit 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 two-digit 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 two-digit integer with first digit 1 (1B<20) can be added to two-digit 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 two-digit numbers and AAA is a thre  [#permalink]

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New post 16 Aug 2012, 10:11
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 two-digit numbers and AAA is a thre  [#permalink]

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New post 16 Aug 2012, 10:14
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rajathpanta wrote:
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??


82+19=101, not 111.

As for 111: since AB and CD are two-digit integers, their sum can give us only one three digit integer of a kind of AAA: 111.
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Re: AB + CD = AAA, where AB and CD are two-digit numbers and AAA is a thre  [#permalink]

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New post 17 Aug 2012, 21:10
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 two-digit numbers and AAA is a thre  [#permalink]

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New post 18 Aug 2012, 00:24
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ratinarace wrote:
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?


AAA is a 3-digit number with all 3 digits alike, so it could be: 111, 222, 333, ..., 999. But the sum of any two 2-digit numbers cannot be more than 99+99=198, so AB+CD can only be 111.
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Re: AB + CD = AAA, where AB and CD are two-digit numbers and AAA is a thre  [#permalink]

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New post 25 Feb 2014, 19:43
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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 two-digit numbers and AAA is a thre  [#permalink]

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New post 27 Mar 2014, 23:56
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\(AB + CD = AAA\)

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 two-digit numbers and AAA is a thre  [#permalink]

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New post 13 Jun 2015, 02:35
surendar26 wrote:
AB + CD = AAA, where AB and CD are two-digit 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 steps

Step 1: AB + CD = AAA i.e. Sum of two 2-digit numbers is a three digit number but sum of two 2-digit number must be less than 200 hence the 3-Digit number must have Hundreds digit as 1 i.e. A = 1

Step 2: If one 2-Digit 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 two-digit numbers and AAA is a thre  [#permalink]

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New post 15 Jun 2015, 04:46
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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 two-digit numbers and AAA is a thre  [#permalink]

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New post 20 Jul 2017, 02:45
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 two-digit numbers and AAA is a thre  [#permalink]

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New post 20 Jul 2017, 04:50
gps5441 wrote:
Please ignore

One thing i am clear that the no has to be 111. But why is 24+87=111 wrong?


AB + CD = AAA.

The tens digit in AB and the digits in AAA are the same. So, A = 1. All this is explained here: https://gmatclub.com/forum/ab-cd-aaa-wh ... l#p1110751
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Re: AB + CD = AAA, where AB and CD are two-digit numbers and AAA is a thre  [#permalink]

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New post 25 Nov 2017, 09:18
Bunuel

Is 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 two-digit numbers and AAA is a thre  [#permalink]

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New post 25 Nov 2017, 09:48
mrinal0308 wrote:
Bunuel

Is this a GMAT like question?
What is the actual source of this question?


Don't know the source but the question is quite GMAT-like.

Check other Addition/Subtraction/Multiplication Tables problems from our Special Questions Directory
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Re: AB + CD = AAA, where AB and CD are two-digit numbers and AAA is a thre  [#permalink]

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New post 10 Dec 2018, 04:31
navigator123 wrote:
AB + CD = AAA, where AB and CD are two-digit 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



chetan2u

Please help.

The question says that AAA is a 3-digit 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 two-digit numbers and AAA is a thre  [#permalink]

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New post 10 Dec 2018, 05:03
ParthSanghavi wrote:
navigator123 wrote:
AB + CD = AAA, where AB and CD are two-digit 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



chetan2u

Please help.

The question says that AAA is a 3-digit 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 3-digit number and A is a distinct digit, this means that the 3 digits in AAA are all As.
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Re: AB + CD = AAA, where AB and CD are two-digit numbers and AAA is a thre &nbs [#permalink] 10 Dec 2018, 05:03
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