The ratio of cupcakes to children at a particular birthday

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The ratio of cupcakes to children at a particular birthday [#permalink]

09 Dec 2012, 08:54

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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

[Reveal] Spoiler: OA

Last edited by Bunuel on 09 Dec 2012, 09:19, edited 1 time in total.

Edited the question.

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Re: The ratio of cupcakes to children at a particular birthday [#permalink]

09 Dec 2012, 09:34

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mun23 wrote:

Given that:
The ratio of cupcakes to children is 104 to 7 --> \frac{cupcakes}{children}=\frac{104k}{7k};

Each child eats exactly x cupcakes --> the number of cupcakes eaten 7kx and the number of cupcakes that remain uneaten is 104k-7kx;

The number of cupcakes that remain uneaten is less than the number of children --> 104k-7kx<7k --> x>13\frac{6}{7} --> x=14 (notice that x cannot be more than 14 since in this case 7kx>104k, which would mean that more cupcakes were eaten than there were).

Now, if x=14, then the number of cupcakes that remain uneaten is 104k-7k*14=6k, thus the number of uneaten cupcakes must be a multiple of both 2 and 3.

Answer: D.
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Re: The ratio of cupcakes to children at a particular birthday [#permalink] 09 Dec 2012, 09:34

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The ratio of cupcakes to children at a particular birthday

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The ratio of cupcakes to children at a particular birthday

The ratio of cupcakes to children at a particular birthday

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