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AB + CD = AAA, where AB and CD are two-digit numbers and AA [#permalink]
 06 Aug 2012, 10:57
Question Stats:
64% (02:06) correct
35% (01:25) wrong based on 3 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? (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 AA [#permalink]
06 Aug 2012, 11:06
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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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Senior Manager
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Re: AB + CD = AAA, where AB and CD are two-digit numbers and AA [#permalink]
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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GMAT Club team member
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Re: AB + CD = AAA, where AB and CD are two-digit numbers and AA [#permalink]
16 Aug 2012, 11:14
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Manager
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Re: AB + CD = AAA, where AB and CD are two-digit numbers and AA [#permalink]
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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GMAT Club team member
Joined: 02 Sep 2009
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9536
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Re: AB + CD = AAA, where AB and CD are two-digit numbers and AA [#permalink]
18 Aug 2012, 01:24
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Re: AB + CD = AAA, where AB and CD are two-digit numbers and AA [#permalink]
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 two-digit numbers and AA
[#permalink]
10 Nov 2012, 06:47
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