Question

If 7a3b5 divisible by 99 for (where a, b are single digit whole numbers)

• A. one pair of (a, b)
• B. two pairs of (a, b)
• C. three pairs of (a, b)
• D. no value of (a, b)

Answer 1

Answer: (D)

no value of (a, b)

$7a3b5$ divisible by $99.$

Means$,$ $7a3b5$ divisible by $9.$

And $7a3b5$ divisible by $11.$

For divisibility by $9,$ we have$,$

$7+a+3+b+5=15+a+b.$

To make it divisible by $9.$

The possible value will be $1$

and possible value of $b$ be $2.$

Hence $71325$ would be the $No.$

but it is not divisible by $11.$

Hence whatever be the value of $(a,b)$ . It will not satisfy both condition i$.$e$,$ It should be divisible by $9$ and $11.$