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A, B, C are digits where A×B is not zero. If AB, BA are both two-digit 27 Apr 2022, 09:00
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75% (hard)

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49% (01:53) correct 51% (02:30) wrong based on 150 sessions

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A, B, C are digits where A×B is not zero. If AB, BA are both two-digit numbers and AAC is a three-digit number, what is the value of B?

(1) AB + BA = AAC
(2) A = 1
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A, B, C are digits where A×B is not zero. If AB, BA are both two-digit 27 Apr 2022, 09:28
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Statement 1
Only A=1, B=9, C=0 satisfy the condition
19+91=110
Sufficient

Statement 2
We don't know anything about B
Insufficient

Ans is A

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shantanugaware
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A, B, C are digits where A×B is not zero. If AB, BA are both two-digit 29 Apr 2022, 00:53
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ankitgoswami
Statement 1
Only A=1, B=9, C=0 satisfy the condition
19+91=110
Sufficient

Statement 2
We don't know anything about B
Insufficient

Ans is A

Posted from my mobile device
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How did you found those values? Did you use any method to find, or was it just trial and error?
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A, B, C are digits where A×B is not zero. If AB, BA are both two-digit 29 Apr 2022, 02:45
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shantanugaware
ankitgoswami
Statement 1
Only A=1, B=9, C=0 satisfy the condition
19+91=110
Sufficient

Statement 2
We don't know anything about B
Insufficient

Ans is A

Posted from my mobile device
How did you found those values? Did you use any method to find, or was it just trial and error?
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shantanugaware

From (1) we can deduce the value of A. Two numbers with two digits each that are added together to give a three digit number can only have 1 as the hundredth digit. Think about it this way: the max value a two digit number can have is 99.\( 99+99 = 198\), and there the hundredth digit is 1 so A must be 1.

Plugging in the value for A will give: \(1B + B1 = 11C\). Looking at this, the only the possible value that B can be is 9. If B is 8 or lower we end up with only a two digit number. Plugging in 9 for B gives: \(19 + 91 = 110\). :)
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A, B, C are digits where A×B is not zero. If AB, BA are both two-digit 06 Jan 2025, 01:09
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