MGMAT CAT Quant Question: Remains

[jeffmoccia]

Problem:
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?

A) 24
B) 21
C) 20
D) 17
E) 15

The MGMAT explanation states y > 6 and b> 9, but why could they not be y > or = 6 and b > or = 9?

For instance, is x were 5 and y were 6, x divided by y would be 0 R 6

[rohit801]

When x is divided by y and there is remainder r, then what it means is: x = yM + r, where M=0,1,2....and y>r

Ex: 8/5 => 8 = 5(1) + 3 as 5 goes into 8 just once, leaving 3 as the remainder.

in your case: 5/6 => 5 = 6(0) + 5, that is the remainder will be 5.

The Divisor has to be greater than the remainder. Ex:

13/4 => 13=4(3) + 1 ..here 4>1.

Sure, we can 13 as 4(2) + 5 BUT if we mean to evaluate 13 divided by, i.e., 13/4 then 13 = 4(3) +1.

Hope that helps.....

[jeffmoccia]

Helps a lot- looking back my question probably doesn't even warrant a response :).

[RonPurewal]

For instance, is x were 5 and y were 6, x divided by y would be 0 R 6

you've got this a little bit twisted -- 5 divided by 6 actually gives a remainder of 5, not 6.
to illustrate this fact, consider a problem in which you have 5 beer cans, and you're trying to make six-packs. in this case, you will get 0 six-packs, and you will have 5 beer cans left over -- hence the remainder of 5.

in general, if x is smaller than y, then dividing x by y will give a remainder of x.