When a positive integer b is divided

[actleader]

question is from GoGMAT prep course.
When a positive integer b is divided by another positive integer a, the remainder is r. What is the remainder when 3b is divided by 3a?

[RonPurewal]

question is from GoGMAT prep course.
When a positive integer b is divided by another positive integer a, the remainder is r. What is the remainder when 3b is divided by 3a?

hi,
you'll need to show us some of your own work on this problem before we discuss it. i.e., you can't just throw a problem on the forum with no commentary; you need to tell us what you tried to do with it. what methods did you try? where did you get stuck? etc.

hint: for this one, try plugging in specific numbers for the variables, and you should be able to figure out what's going on fairly quickly.

[actleader]

Ron, I met the following solution of the problem
When b is divided by a, the remainder is r. We can represent b as b = ka + r, where k is some integer. Now, 3b equals 3ka + 3r . Hence dividing 3b by 3a yields
(3b/3a)=(3ka+3R)/3a=(k+3r)/3a, where 3r is the remainder.

Unfortunatelly I cant understand how 3r can be the remainder in such a case

[tim]

please do what Ron suggested and plug in some numbers to convince yourself. also note that *by definition* the remainder is the 3r that is added on the right side of the equation..

[actleader]

Ron's advice is approachable,
having substitute some numbers the solution became obvious

(A) 1
(B) 3(b + ar)
(C) 3(b − ar)
(D) 3r − b
(E) 3r

but I'd like to approach the method without PI,
and the explanation provided above is not understandable :(

how can we get (k+3r)/3a from (3ka+3r)/3a?

[jnelson0612]

Ron's advice is approachable,
having substitute some numbers the solution became obvious

(A) 1
(B) 3(b + ar)
(C) 3(b − ar)
(D) 3r − b
(E) 3r

but I'd like to approach the method without PI,
and the explanation provided above is not understandable :(

how can we get (k+3r)/3a from (3ka+3r)/3a?

Seriously, why would you NOT want to plug in? It's quick, it's easy, and you can do the problem in less than a minute! Often it doesn't make sense to come up with the most elaborate mathematical way to do the problem. You just want to find the most efficient way to the correct solution.