mun23 wrote:
The ratio of cupcakes to children at a particular birthday party is 104 to 7. Each child at the birthday party eats exactly x cupcakes (where x is a positive integer) and the adults attending the birthday party do not eat anything. If the number of cupcakes that remain uneaten is less than the number of children at the birthday party, what must be true about the number of uneaten cupcakes?
I. It is a multiple of 2.
II. It is a multiple of 3.
III. It is a multiple of 7.
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II and III
Another approach is to use numbers and reasoning.
The less number to create the ratio
# Cupcakes (C)=104
# Children or kids (K) =7
C/k =104/7
After each kid has eaten x cupcakes the number left was less than # of kids. It means leftover (uneaten) is less than 7. It is between 1-6 cupcake.
Based on above we can eliminate choices C & E. 1 to 6 can't be multiple of 7
Now we need to work backward to find the number eaten by kids and the number should divide into 7. With sense of numbers 105 divides into 7. The next number divides into 7 is 98. We do not need to continue as uneaten cupcakes not huge.
Let uneaten cupcakes = 6
104 - 6 =98 ...........Hence the whole kids ate 98 cupcakes then each kid must have eaten x= 14 cupcakes
104- 5= 99.............x can't divide into 7
No need to continue till 1 as there is no number divides into 7 between 98 & 105
Hence uneaten cupcakes (6) should multiple of 2 & 3
Answer: D