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# A grocery store wanted to repackage all of the eggs that

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Intern
Joined: 20 Oct 2009
Posts: 12
A grocery store wanted to repackage all of the eggs that  [#permalink]

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12 Jun 2010, 08:08
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Difficulty:

45% (medium)

Question Stats:

65% (00:55) correct 35% (01:07) wrong based on 62 sessions

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A grocery store wanted to repackage all of the eggs that were in cartons that each contaon 30 eggs into smaller cartons that would each contain 12 eggs. How many of the smaller cartons would be required tp hold all of the eggs.

(1) The number of smaller cartons needed is 15 more than the number of larger cartons.
(2) The number of large carton is 10
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Joined: 02 Sep 2009
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12 Jun 2010, 08:23
Other wrote:
Q: A grocery store wanted to repackage all of the eggs that were in cartons that each contaon 30 eggs into smaller cartons that would each contain 12 eggs. How many of the smaller cartons would be required tp hold all of the eggs.
1) The number of smaller cartons needed is 15 more than the number of larger cartons.
2) The number of large carton is 10

Let $$x$$ be the # of large cartons and $$y$$ the # of small cartons.
Given: $$30x=12y$$. Question $$y=?$$

(1) The number of smaller cartons needed is 15 more than the number of larger cartons --> $$x=y-15$$ --> $$30(y-15)=12y$$ --> $$y=25$$. Sufficient.

(2) The number of large cartons is 10 --> $$x=10$$ --> $$30x=300=12y$$ --> $$y=25$$. Sufficient.

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Re: A grocery store wanted to repackage all of the eggs that  [#permalink]

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09 Dec 2017, 16:41
1
Hi All,

We're told that the eggs in cartons that each contain 30 eggs are going to be moved into smaller cartons that would each contain 12 eggs. We're asked for the number of smaller cartons required tp hold all of the eggs. This question can be solved in a couple of different ways, so here's an approach that uses a bit of 'brute force' and some basic arithmetic. Fact 2 is considerably easier to deal with than Fact 1, so I'm going to start there:

2) The number of large carton is 10.

With 10 large cartons, and 30 eggs per large carton, we know that we have (10)(30) = 300 eggs. Thus, we can clearly figure out how many smaller cartons we would need. While you don't technically have to do that math to know that Fact 1 is SUFFICIENT, here it is:
300/12 = 25 small cartons
Fact 2 is SUFFICIENT

1) The number of smaller cartons needed is 15 more than the number of larger cartons.

Now that we have the information in Fact 1 to use as a reference, we can see one obvious example of the number of smaller cartons being 15 MORE than the number of larger cartons:
10 large cartons of eggs = 25 small cartons of eggs

The question now is whether there are any other 'combinations' that will lead to exactly 15 more smaller cartons needed:

9 large cartons of eggs = 9(30) = 270
270/12 = 22.5 small cartons... you can't have "half a small carton", so we would need 23 small cartons to hold those eggs.
9 large cartons --> leads to 23 small cartons needed.... but that's a difference of 14 cartons (and we need it to be 15 cartons). This is clearly NOT a possible option since the results don't 'fit' what we're told.

11 large cartons of eggs = 11(30) = 330
330/12 = 27.5 small cartons... you can't have "half a small carton", so we would need 28 small cartons to hold those eggs.
11 large cartons --> leads to 28 small cartons needed.... but that's a difference of 17 cartons (and we need it to be 15 cartons). This is clearly NOT a possible option since the results don't 'fit' what we're told.

Looking at the data we have, it seems clear that with each large carton of eggs we add, we end up needing even more and more small cartons. Thus, there's only ONE option in which the difference in cartons is 15... when there are exactly 10 large cartons.
Fact 1 is SUFFICIENT

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Re: A grocery store wanted to repackage all of the eggs that &nbs [#permalink] 09 Dec 2017, 16:41
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