remainder

[thephoenix]

x, y, a, and b are positive integers. When x is divided by y, the remainder is 6. When a is divided by b, the remainder is 9. Which of the following is NOT a possible value for y + b?
24
21
20
17
15
how to solve this
whats the funda????

[albatross86]

If the remainder when X is divided by Y is 6, Y cannot be less than 7. This is because a number less than 7 can never yield a remainder of 6.

In short the takeaway is, the maximum remainder when dividing my N is N-1.

Thus for x/y to give remainder 6, y must be >= 7
For a/b to give a remainder 9, b must be >=10

Thus Minimum value of y + b = 7 + 10 =17

Thus 15 is not a possible value.

[thephoenix]

If the remainder when X is divided by Y is 6, Y cannot be less than 7. This is because a number less than 7 can never yield a remainder of 6.

In short the takeaway is, the maximum remainder when dividing my N is N-1.

Thus for x/y to give remainder 6, y must be >= 7
For a/b to give a remainder 9, b must be >=10

Thus Minimum value of y + b = 7 + 10 =17

Thus 15 is not a possible value.

gr8 concept
many thanks