Well, if the remainder is 102 when K is divided by 1602, K could certainly be equal to 102, in which case the remainder will be 13 when K is divided by 89. And, because the answer choices are all numbers (we don't have the answer 'cannot be determined exactly') if the remainder is 13 for one suitable value of K, it must be 13 for any suitable value of K, since this is a GMAT question; one of the answers must be correct.Brent Hanneson wrote:When positive integer K is divided by 1602, the remainder is 102. What is the remainder when K is divided by 89?
(A) 0
(B) 13
(C) 18
(D) 34
(E) 51
Ian raises a very important point about finding numbers to plug into questions involving remainders.Well, if the remainder is 102 when K is divided by 1602, K could certainly be equal to 102
Great thread. Invaluable information.Brent Hanneson wrote:Ian raises a very important point about finding numbers to plug into questions involving remainders.Well, if the remainder is 102 when K is divided by 1602, K could certainly be equal to 102
Often, when students are given information about remainders, they begin examining numbers that are larger than the divisor. For example, if n is divided by 6, the remainder is 5, most students recognize that n could equal 11, 17, 23, etc, but they often fail to recognize that n might also equal 5.
There is an error in the explanation. Still a very good explanationDanaJ wrote:well you have k = 1602*n+102.
All you have to notice, IMHO, is that 1602 = 2 *801 = 2(890-89)=2*9*89. So k = 2*9*89*n + 102 = 89(2*9*n+1) +13. That means that the remainder will be 13.
