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AB + CD = AAA, where AB and CD are twodigit numbers and AA [#permalink]
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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 AA [#permalink]
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06 Aug 2012, 11:06
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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 AA [#permalink]
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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 AA [#permalink]
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16 Aug 2012, 11:14



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Re: AB + CD = AAA, where AB and CD are twodigit numbers and AA [#permalink]
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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 AA [#permalink]
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18 Aug 2012, 01:24
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Re: AB + CD = AAA, where AB and CD are twodigit numbers and AA [#permalink]
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10 Nov 2012, 06:47
Bunnuel, is there any algebraic approach to this? Please help out Brother Karamazov



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Re: AB + CD = AAA, where AB and CD are twodigit numbers and AA [#permalink]
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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 AA [#permalink]
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06 Oct 2015, 03:19
the greatest 2 digit number is 99 so 99+99 =198... thats shows that AAA can not be 222 or 333 or ...... 999, it has to be 111.... now that aaa is 111,ab+cd=aaa ... a bit of logic, a=1 and c=9...
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Re: AB + CD = AAA, where AB and CD are twodigit numbers and AA [#permalink]
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18 Mar 2017, 10:29
we can get there by trying numbers: AB CD AAA first what come to my mind is that A can be 1, hence B+D=11, then 1(A) + 9 (C)=10 + 1 Answer is D



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AB + CD = AAA, where AB and CD are twodigit numbers and AA [#permalink]
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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 AA [#permalink]
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20 Jul 2017, 05:50



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Re: AB + CD = AAA, where AB and CD are twodigit numbers and AA [#permalink]
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21 Jul 2017, 05:11



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Re: AB + CD = AAA, where AB and CD are twodigit numbers and AA [#permalink]
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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 AA [#permalink]
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25 Nov 2017, 10:48



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Re: AB + CD = AAA, where AB and CD are twodigit numbers and AA [#permalink]
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19 Jan 2018, 03:56
This is how I solved it.
There are 2 options:
Option 1: B + D = A, in that case : A+C = 10A+A => C = 10A (this is impossible knowing that max value of C is 9 and min value is 0)
Option 2: B+D = 10A (which means 1 carries over), in that case: A+C+1 = 10A+A => C= 10A 1 (only 1 solution possible where A = 1 and C = 9)
Hope this helps !



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Re: AB + CD = AAA, where AB and CD are twodigit numbers and AA [#permalink]
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19 Jan 2018, 06:38
Since the only possible value for AAA is 111, therefore A will always be 1. Now AB is in the range of 10 to 19 according to this fact but if we subtract 10 or 11 from 111, we get triple digit number. So lets just take max and minimum possible value of AB, that would be 12 and 19 respectively. Now if you subtract 12 from 111 you would get 99 and if you subtract 19 from 111 you get 92. (92 and 99 are max and min value of CD). Therefore C's value will always be 9.




Re: AB + CD = AAA, where AB and CD are twodigit numbers and AA
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19 Jan 2018, 06:38






