When the positive integer M is divided by the positive integer y, the

Tricky one if we miss the basics. Find below detailed explanation

When the positive integer M is divided by the positive integer y, the quotient is 11 and the remainder is z. => \(M =11y+z\)
=> Here \(z < y\) (That's the case only then reminder can be z)

When you divide z by y, the remainder is 9. => as \(z < y\) and when z is divided by y remainder is 9 => \(z=9\)

So our equation is \(M =11y +9\) for \(z<y\)

Which of the following could be the value of M ?
So lets write all the numbers in form of above equation. If it satisfies the equation than value can be equal to M
So general steps for such kind of questions : Subtract 9 from number and see if its a multiple of 11. if condition satisfies then number can be value of M


1. 108
=> 108 - 9 =99 so as 99 is multiple of 11 this can be our answer. Wrong
Lets write it in equation form : 108 = 11*9 +9 . So if we compare it with M=11y + z => y=z=9 not possible as z<y always
So this value is not M

2. 119
=> 119 - 9 =110 so as 110 is multiple of 11 this can be our answer.
Lets write it in equation form : 119 = 11*10 +9 . So if we compare it with M=11y + z => y=10 and z =9 => z<y satisfies our equation
So this can be value of M

3. 20
=> 20 - 9 =11 so as 11 is multiple of 11 this can be our answer. Wrong
Lets write it in equation form : 20 = 11*1 +9 . So if we compare it with M=11y + z => y=1 and z =9 => z>y. This can't be true as by our equation z<y always
So this value is not M

4. 30
=> 30 -9 =21 This cant be written in multiple of 11.
So this value is not M

A) 1, 2 and 3
b) 1 and 2 only
c) 3 only
d) 1, 2, 3 and 4
e) 2 only

Answer: E