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# The ratio of cupcakes to children at a particular birthday

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Manager
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The ratio of cupcakes to children at a particular birthday [#permalink]  22 Jul 2007, 15:13
The ratio of cupcakes to children at a particular birthday party is 104 to 7. Each chiled at the birthday party eats exactly x cupcakes (where x is a positive integer) and the adults attending the birthday paraty do not ear 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.

Pick which applies.

I do not know how to approach this question thanks.
Senior Manager
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[#permalink]  22 Jul 2007, 15:57
They must have had 14 cupcakes each.

7*14 = 98. Remaining uneaten is 6x.

So, I and II are true.
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[#permalink]  23 Jul 2007, 10:42
ioiio wrote:
They must have had 14 cupcakes each.

7*14 = 98. Remaining uneaten is 6x.

So, I and II are true.

How did u get that ?

Let the ratio be 104y:7y

Now 104y - 7yx <7y> 1

Now if we go on to solve for x we get x > 97/7. But we need to make our decision based on equation 1.

I dont see any of the 3 choices to be absolutely true.

nfa1rhp can u post the original OE ?
Manager
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[#permalink]  23 Jul 2007, 11:22
ioiio wrote:
They must have had 14 cupcakes each.

7*14 = 98. Remaining uneaten is 6x.

So, I and II are true.

Not exactly. If there were 7 children, the cupcakes would be 728.
If each child ate 14 we would have 630 left, which is more than 7!!
I think we need less than 728-7 to be consumed or 722.
Number left-6. In this case I and II stand.

Seems like I and II.

What is OA?
Manager
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[#permalink]  23 Jul 2007, 12:49
Hayabusa, I think you missed the part of the problem where it said that the ratio is 104 cupcakes per every 7 children. Not 104 cupcakes per child (talk about a sugar rush!)

I think I know where ioiio was trying to go with that. If you divide 104 by 7, you get that each child would get a minimum of ~14.85 cupcakes, or 14 whole cupcakes (assuming that there is a minimum of 7 children and 104 cupcakes).

Then, if you multiply the 14 whole cupcakes by the 7 children you come up with 98 whole cupcakes, meaning that you'd have 6 leftover cupcakes. So, by this logic, since 2 (I.) and 3 (II.) are both multiples of 6, then I and II would be true. I have no idea if this would hold true if there were more children.

I have absolutely no idea if this is right, or even in the right ballpark. Is the OA available?
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[#permalink]  23 Jul 2007, 12:59
ishcabibble wrote:
Hayabusa, I think you missed the part of the problem where it said that the ratio is 104 cupcakes per every 7 children. Not 104 cupcakes per child (talk about a sugar rush!)

I think I know where ioiio was trying to go with that. If you divide 104 by 7, you get that each child would get a minimum of ~14.85 cupcakes, or 14 whole cupcakes (assuming that there is a minimum of 7 children and 104 cupcakes).

Then, if you multiply the 14 whole cupcakes by the 7 children you come up with 98 whole cupcakes, meaning that you'd have 6 leftover cupcakes. So, by this logic, since 2 (I.) and 3 (II.) are both multiples of 6, then I and II would be true. I have no idea if this would hold true if there were more children.

I have absolutely no idea if this is right, or even in the right ballpark. Is the OA available?

Oooops Absolutely! I owe ioiio an apology.

Still, I and II make sense to me.
Manager
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[#permalink]  23 Jul 2007, 14:53
I agree that it's I and II, for the same reasoning - that 104/7=14, r6. If 104:7 is the ratio, the remainder would always be a multiple of 6. (208/14=14, r12, 312/21=14,r18 etc....)
Senior Manager
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[#permalink]  23 Jul 2007, 14:54
ishcabibble wrote:
Hayabusa, I think you missed the part of the problem where it said that the ratio is 104 cupcakes per every 7 children. Not 104 cupcakes per child (talk about a sugar rush!)

I think I know where ioiio was trying to go with that. If you divide 104 by 7, you get that each child would get a minimum of ~14.85 cupcakes, or 14 whole cupcakes (assuming that there is a minimum of 7 children and 104 cupcakes).

Then, if you multiply the 14 whole cupcakes by the 7 children you come up with 98 whole cupcakes, meaning that you'd have 6 leftover cupcakes. So, by this logic, since 2 (I.) and 3 (II.) are both multiples of 6, then I and II would be true. I have no idea if this would hold true if there were more children.

I have absolutely no idea if this is right, or even in the right ballpark. Is the OA available?

Sorry Guyz. I dont get to check the forums at work. Yeah! you were right about how I got that solution.

I should have explained better. I have been solving these GMAT problems for all of two days now. I am yet to get used to the jargon used here and sometimes have no clue whether any of my ramblings make sense to others or not

Will get better in a few days. I promise

Btw, whats the OA?
Manager
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[#permalink]  24 Jul 2007, 17:13
Sorry all, the the correct answer OA? I and II only thank you all.
[#permalink] 24 Jul 2007, 17:13
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# The ratio of cupcakes to children at a particular birthday

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