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by kanha81 » Wed Mar 04, 2009 10:46 am
q: tom spent day in baking cookies. of the first 3 dozen he baked, 1/3 contained chocolate chip cookies. of the remaining, 1/2 contained chocolate chip cookies. How many total chocolate chip cookies did he bake?

1) Tom baked 5 dozen cookies
2) Of all the cookies Tom baked, two fifths contained chocolate chip cookies

My question is what about the remaining 2 dozen cookie. Is there not a possibility that those 24 cookies can also contain chocolate chip cookies on top of the the first 3 dozen which contains 24 chocolate chip cookies?

Can you explain the classic part 2 word translation?
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by shargaur » Wed Mar 04, 2009 11:42 am
q: tom spent day in baking cookies. of the first 3 dozen he baked, 1/3 contained chocolate chip cookies. of the remaining, 1/2 contained chocolate chip cookies. How many total chocolate chip cookies did he bake?

1) Tom baked 5 dozen cookies
2) Of all the cookies Tom baked, two fifths contained chocolate chip cookies

St. 1 ) he baked 5 dozen cookies. In first 3 dozens 1/3 were choclate = 12
and in last 2 dozens 1/2 was choclate = 12 total =24
Sufficient : So Ans : A D

St 2) how many total cookies he baked = unknown so insufficient

Hence A
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by Feep » Wed Mar 04, 2009 4:41 pm
Shargaur is (at least, in my humble opinion) incorrect.

A is obviously sufficient, as shown by the above reasoning.

B is also sufficient, however. We know the overall ratio of cookies must be 2/5th. We know how many were chocolate chip in the first three dozen, but we ALSO know a fixed ratio of the remaining cookies. In other words, at three dozen, the ratio was 1/3. As more cookies are made, this ratio will steadily climb until, at infinity cookies made, it will reach 1/2. Obviously 2/5 is within this range, so there must be a very particular amount of cookies made so that this proposition is true. (Additional note: your reasoning on the test should end here; you have shown that this information is sufficient. Actually solving the problem will take at least sixty seconds more in most cases, especially if you aren't great at algebraic manipulation.)

Let us call x the number of cookies made after the first three dozen.

So, 2/5 = cookies with chocolate chips / all cookies

0.4 = (12 + 0.5x) / (36 + x)

Some quick algebra, and x is shown to be equal to 24 cookies.

Total chocolate chip cookies = 12 + 0.5(24) = 24 chocolate chip cookies, out of 60 total. 24/60 = 2/5.

So the answer is D.
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