CaptainGMAT wrote:

The ratio of cupcakes to children at a party is 27 to 7. Each child at the party eats exactly x

cupcakes, where x is a positive integer, after which a total of y cupcakes remain uneaten. If y is

less than the number of children at the birthday party, which of the following must be true?

I. y is a multiple of 2.

II. y is a multiple of 3.

III. y is a multiple of 7

(A) I only

(B) II only

(C) III only

(D) I and II only

(E) I, II and III

OA seems to be wrong, the number of cupcakes will always be a multiple of 3 and 2.

For Example: Consider 27 cupcakes and 7 Children:

Given Cupcakes remaining is less than number of Children. Therefore only combination is 3 Cupcakes per Child leaves 6 Cupcakes which is multiple of 3 and 2 only.

Same goes for 54 cupcakes and 14 Children.