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AB + CD = AAA, where AB and CD are 2 digit numbers and AAA [#permalink]
08 Jun 2005, 10:32

00:00

A

B

C

D

E

Difficulty:

25% (medium)

Question Stats:

71% (02:34) correct
29% (01:11) wrong based on 82 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: Number properties - PS [#permalink]
09 Jun 2005, 07:57

1

This post received KUDOS

smcgrath12 wrote:

AB + CD = AAA, where AB and CD are 2 digit numbers and AAA is a 3 digit number. A,B,C and D are distinct positive numbers. In the above addition problem, what is the value of C?

The sum of two 2 digit numbers cannot be more than 200. Hence A had to be 1.

Yep, thats right. Can you please explain how you got that? These kinda questions always stumps me.

AB +
CD =
AAA

We know that A must be 1 since A + C (+1 maybe)= AA
(+1 maybe) means that an extra unit can be carried over from summing B and D.
The largest number AA can be cannot exceed 19.

Now since A=1 1+C = 11, C cannot be 10, so we need one unit to be carried over from B+D so C equals 9.

p.s. there are multiple combinations for B and D as long as B+D = 11

Re: Number properties - PS [#permalink]
09 Jun 2005, 02:28

smcgrath12 wrote:

AB + CD = AAA, where AB and CD are 2 digit numbers and AAA is a 3 digit number. A,B,C and D are distinct positive numbers. In the above addition problem, what is the value of C?

from AB+CD=AAA:
B+D=10+A
A+C+1=10A+A -> C+1=10A
A has to be 1 as if the sum of two 2-digit numbers equals a 3-digit number, the max that the 3-digit number can be is 198...
if A=1, C=9

Re: AB + CD = AAA, where AB and CD are 2 digit numbers and AAA [#permalink]
24 Feb 2014, 08:49

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Re: AB + CD = AAA, where AB and CD are 2 digit numbers and AAA [#permalink]
24 Feb 2014, 10:48

Expert's post

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).