Question

If a five-digit number 7xy73 is divisible by 99, then find the value of (3x + 2y). plz help

Answer 1

To solve this problem, we can use divisibility rules.

So the number is exactly divisible by 99, which means it is divisible by 9 and 11 since we can write 99 as:

[tex]\mathtt{99 = 9 × 11 }[/tex]

So, according to the divisibility rules for 9:

$\mathtt{2 + 3 + A + B + 3 =}$ $\sf{some~ multiple~ of~ 9}$  

$\sf{So,}$$\mathtt{ A + B = 1 ~or~ A + B = 10}$

And according to the divisibility rules for 11:

$\mathtt{2+A+3 - 3 + B = 2 + A - B =  0 ~or~ 11}$

[tex]\mathtt{or~ A - B = 9~ or~ A - B = -2 }[/tex]

Well, A - B = 9 is not possible if A and B are single digit positive integers and A + B is either 1 or 10.

$\mathtt{So, A - B = -2}$$\sf{ must~ be~ true.}$

And if that is true,  cannot be 1 if they both have to be positive integers.

$\mathtt{So~A + B = 10}$ $\sf{ ~too,~ must ~be~ true.}$

So, solving these simultaneous equations:

[tex]\mathtt{A + B = 10 }[/tex]

$\mathtt{A - B = -2}$

we get, $\mathtt{2A = 8}$

$\mathtt{A = 4~ and~ B = 6}$

Answer 2

Step-by-step explanation:

the correct answer will be 21