Question

23a7b is divisible by 45 but not by 10. Find the value of a.
A) 1
B)2
C)3
D)4

Answer 1

$\underline{\pink { Divisibility \: Rules: }}$

1. The given number is divisible by 5 ,only if the unit's digit is '0' or '5' .
2. If the unit's digit of a number is '0' ,then it is divisible by 10.
3. The given number is divisible by 9 , only if the sum of the digits is multiple of 9 Or divisible by 9.

$Here, given \: number \: 23\pink {a} 7 \blue {b}$

Condition:

Number 23a7b is divisible by 45 should be divisible by 5 and 9 but not by 10.

$\blue {Last \:digit \: must \:be \: 5 .} \\\orange { ( It \: should \:not \: divisible \:by \: 10 ) }$

$\green { b = 5 }$

$Now, Sum \:of \:the \:digits \\= 2+3+a+7+5 \\= 17+a \: ( Must \: be \: divisible \:by \: 9 )$

$If \:we \: take \: a = 1 \implies sum \: divisible \:by \: 9$

Therefore.,

$Option \: \pink { ( A ) } \:is \: correct.$

•••♪