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AB + CD = AAA, where AB and CD are two-digit numbers and AA [#permalink]
06 Aug 2012, 09:57

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Difficulty:

35% (medium)

Question Stats:

73% (02:17) correct
27% (01:47) wrong based on 123 sessions

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?

Re: AB + CD = AAA, where AB and CD are two-digit numbers and AA [#permalink]
06 Aug 2012, 10:06

2

This post received KUDOS

Expert's post

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).

Re: AB + CD = AAA, where AB and CD are two-digit numbers and AA [#permalink]
18 Aug 2012, 00:24

1

This post received KUDOS

Expert's post

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. _________________

Re: AB + CD = AAA, where AB and CD are two-digit numbers and AA [#permalink]
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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