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Joined: 07 Apr 2014
Status:Math is psycho-logical
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Location: Netherlands
GMAT Date: 02-11-2015
WE:Psychology and Counseling (Other)
Re: AB + CD = AAA, where AB and CD are two-digit 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.