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Manager
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AB + CD = AAA, where AB and CD are 2 digit numbers and AAA [#permalink]
 08 Jun 2005, 11:32
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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?
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Manager
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Yep, thats right. Can you please explain how you got that? These kinda questions always stumps me.
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Director
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smcgrath12 wrote: 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
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Manager
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Think I got it one way.
From AB + CD = AAA, we get 10A + B + 10C + D = 111A
Meaning, 101A = 10C + (B + D) ------------- (A)
Now, there are 2 possibilities,
1) B + D = A. Putting B+D=A in A, we get C = 10A. But that would violate the data given. Even if A=1 (minimum), C=10. So this condition is false.
2) B + D = 10 + A. Putting B+D=10+A in A, we get C = 10A - 1. Now, the only way C < 10, is when A=1.
Thus, we get A=1, C=9.
Any other ways to approach this??
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Current Student
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9 for me...
I just picked AAA=111
then worked my way back, knowing A was 1!
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Senior Manager
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Re: Number properties - PS [#permalink]
09 Jun 2005, 03:28
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
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Senior Manager
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Re: Number properties - PS [#permalink]
09 Jun 2005, 08:57
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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.
Since AB < 20 ( a=1) , CD > 90 , hence C = 9.
HMTG.
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Re: Number properties - PS
[#permalink]
09 Jun 2005, 08:57
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