Playing with numbers

Number Theory Level 2

If the 5-digit number 1 A 2 B 5 ‾ \overline{1A2B5} is divisible by 9, then find the least value of A + B A+B .


The answer is 1.

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4 solutions

Ryan Redz
Jun 2, 2014

divisibility rule: the sum of the digits must be divisible by 9.

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Purnima Sharma
Jun 9, 2015

according to the divisibility rule of 9 , the sum of all digits of the number should be divisible to 9 . here, the sum will be 1+A+2+B+5 =8+A+B now question asked for the least value of A+B so it will be 1 as 8+1 =9 and 9 is divisible by 9 .. :)

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Sanket Panchamia
Jun 18, 2014

Shouldnt the answer be 10? If 1A2B5 is a number, how can A+B be 1?

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The sum of digits of a multiple by nine is a other multiple by nine or nine. The sum 1+2+5+A+B must be a multiple by nine. 1+2+5+A+B=8+A+B. Suppose that A is 0. To get nine B should be 1. Now we have 1A2B5=10215 a multiple by nine. Therefore A+B=0+1=1

Victor Paes Plinio - 6 years, 11 months ago
Temesh Gaikwad
May 17, 2014

sum of digits should be multiple of 9 for no.to be divisible by 9

1+A+2+B+5= 8+A+B= 9x

let x=1,

hence A+B=1

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