If the eight-digit number $5a32465b$ is divisible by $88$, then $2a+ 5b =$

Let me solve this carefully: For divisibility by $88$ $(= 8 × 11)$: Number must be divisible by both $8$ and $11$ $1)$ For divisibility by $8$: - Last three digits $(65b)$ must be divisible by $8$ - Testing values: $b = 6$ makes $656$ divisible by $8$ $2)$ For divisibility by $11$: - Difference of sums of alternate digits must be divisible by $11$ - $(5+3+4+5)-(a+2+6+6)=17-14-a$ - $(3 - a)$ must be divisible by $11$ - Therefore $a = 3$ So the number is $5332465b$ where $b = 6$ $2a + 5b = 2(3) + 5(6)$ $= 6 + 30$ $= 36$