Question from CAT Exam

[walter.hoffman]

Regarding the following question on my CAT exam:

If (x # y) represents the remainder that results when the positive integer x is divided by the positive integer y, what is the sum of all the possible values of y such that (16 # y) = 1?


8

9

16

23

24

The definition given tells us that when x is divided by y a remainder of (x # y) results. Consequently, when 16 is divided by y a remainder of (16 # y) results. Since (16 # y) = 1, we can conclude that when 16 is divided by y a remainder of 1 results.

Therefore, in determining the possible values of y, we must find all the integers that will divide into 16 and leave a remainder of 1. These integers are 3 , 5, and 15. The sum of these integers is 23.

The correct answer is D.

Why is the answer not 24? 1 is an integer. 15*1?

[tim]

1 does not work. 16 divided by 1 does not leave a remainder of 1; it leaves a remainder of 0.