Question

if the 7 - digit number x42132y is divisible by 44, where y ≠ 0, 4, then find the value of (y - x)?​

Answer 1

Answer:

ok,

Step-by-step explanation:

If x3627y0 is divisible by 44, what is the maximum possible value of (x+y)?

What are the new enhancements to the Confluence mobile app?

For the number x3627y0 to be divisible by 44 .

Factorise [math]44[/math such that the factors are prime to each other.

Only option is 44=4×11

Divisibility Rule for 11 :

The sum of the digits at even place is subtracted from the sum of the digits at odd places. If the result is either 0 : or divisible by 11 , then the original number is divisible by 11 .

Now, considering the given problem

Sum of digits at odd places:

Sodd=x+6+7+0=13+x

Sum of digits at odd places:

Seven=3+2+y=5+y

Sodd−Seven=13+x−5−y

Sodd−Seven=8+x−y=0or11 ——- (1)

Divisibility Rule for 4 :

Last two digits of given number should be divisible by 4

That is y0 /4

y can take values as

y=0,2,4,6,8 —————————-(2)

Now, from equation (1) and (2)

we have

or x−y=11−8

x−y=3

x=y+3

For,

y=0;x=3

y=2;x=5

y=4;x=7

y=6;x=9

y=8;x=11 ( cannot be answer, since it is two digit)

From these set of values, we have

max (x+y)=15

x=8+y

Considering this only, we get values of (x,y) as

y=0;x=8

y=2;x=10 ( cannot be answer, since it is two digit)

y=4;x=12 ( cannot be answer, since it is two digit)

y=6;x=14 ( cannot be answer, since it is two digit)

y=8;x=16 ( cannot be answer, since it is two digit)

From these set of values, we have

max (x+y)=8

From both sets, the maximum value of x+y =15

Therefore, the total number of ordered pairs are 4.

hope it helps

thank you ☺✌