A grocery store wanted to repackage all of the eggs that were in carto

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

Let \(x\) be the number of large cartons and \(y\) be the number of small cartons. We are given that \(30x = 12y\), and we need to solve for \(y\).

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

The above implies that \(y = x + 15\)

Substituting this into the equation \(30x = 12y\), we get:

\(30x = 12(x + 15)\)

Simplifying this equation, we get \(x = 10\) and \(y = 25\). Therefore, statement (1) is sufficient.

(2) The number of large carton is 10

The above gives that \(x=10\). Using this information in the equation \(30x = 12y\), we get \(y = 25\). Therefore, statement (2) is also sufficient.

Answer: D.
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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

Final Answer:

GMAT assassins aren't born, they're made,
Rich
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Hi Bunuel,
Why would you assume that there are NO leftovers on the smaller cartons?

Algebraically, why can't it be 30x = 12y + Remainder?

(Therefore the number of smaller cartons would be "y+1")

Greetings,
Kevin

I think, The wording of the problem suggests that this is not the case:

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

Based on the language used in the problem, it appears that we can in fact repackage all of the eggs into smaller packages without any left over.
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