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it is chocolate flavored

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by sanju09 » Fri Jul 30, 2010 4:30 am
When a cookie is taken at random from a jar, what is the probability that it is chocolate flavored?

1. There are twice as many chocolate flavored cookies as there are almond flavored cookies in the jar.
2. One third of the cookies in the jar are almond flavored.

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Source: — Data Sufficiency |
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by selango » Fri Jul 30, 2010 4:46 am
P(CHOC)=Choc/Total

stmt1,

2C=A

We dont know about other flavours info and total values.

Insuff

stmt2,

1/3*x=A

We dont know about other flavours ratios.

Insuff

Combining 1 and 2,

C=2A

A=1/3*x,C=2/3*x

Prob(CHOC)=2/3x/(1/3x+2/3x)=2/3

Suff

Pick C
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by santoostar » Mon Aug 09, 2010 7:31 am
there could be cookies other than almond and chocolate flavour. its no where explictly mentioned that the jar contains only 2 type of cookies...can some one help me with this please!! could be a simple one...but i feel this understanding will help on DS to a great extent.

Thanx in advance.
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by lunarpower » Wed Aug 11, 2010 3:34 am
santoostar wrote:there could be cookies other than almond and chocolate flavour. its no where explictly mentioned that the jar contains only 2 type of cookies...can some one help me with this please!! could be a simple one...but i feel this understanding will help on DS to a great extent.

Thanx in advance.
actually, this statement is incorrect in two different ways.

(1)
ironically, we DO know that there are no other cookies -- precisely because the authors of this question have chosen the only fractions for which we can figure this out.
specifically, if you combine the two statements, you get 1/3 almond and 2/3 chocolate. since 1/3 + 2/3 = 1 = all the cookies in the jar, you know that there cannot be any other varieties of cookies in the jar.

(2)
even if it were possible to have other kinds of cookies in the jar -- e.g., let's say that the jar contains 1/7 almond and 2/7 chocolate cookies, so that the other 4/7 of the cookies in the jar are of mystery flavors -- it still doesn't matter, since all we care about is the fraction of chocolate cookies. in this hypothetical case, that fraction would be 2/7.
takeaway:
in data sufficiency, you are NOT concerned with finding every single quantity in the problem. you are only concerned with finding the ONE quantity for which you are actually ASKED!
Ron has been teaching various standardized tests for 20 years.

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by santoostar » Wed Aug 11, 2010 6:54 am
lunarpower wrote:
santoostar wrote:there could be cookies other than almond and chocolate flavour. its no where explictly mentioned that the jar contains only 2 type of cookies...can some one help me with this please!! could be a simple one...but i feel this understanding will help on DS to a great extent.

Thanx in advance.
actually, this statement is incorrect in two different ways.

(1)
ironically, we DO know that there are no other cookies -- precisely because the authors of this question have chosen the only fractions for which we can figure this out.
specifically, if you combine the two statements, you get 1/3 almond and 2/3 chocolate. since 1/3 + 2/3 = 1 = all the cookies in the jar, you know that there cannot be any other varieties of cookies in the jar.

(2)
even if it were possible to have other kinds of cookies in the jar -- e.g., let's say that the jar contains 1/7 almond and 2/7 chocolate cookies, so that the other 4/7 of the cookies in the jar are of mystery flavors -- it still doesn't matter, since all we care about is the fraction of chocolate cookies. in this hypothetical case, that fraction would be 2/7.
takeaway:
in data sufficiency, you are NOT concerned with finding every single quantity in the problem. you are only concerned with finding the ONE quantity for which you are actually ASKED!
Thank you so much Ron for the explanation. It did clear my confusion.

Suppose we had the statement 1 andd 2 read

1. There are twice as many chocolate flavored cookies as there are almond flavored cookies in the jar.

2- One fifth of the cookies in the jar are almond flavored.

then, will the answer still be C?

My understanding says it would be E - correct me if i am wrong...( sorry if confused any1)..

Santo

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by lunarpower » Thu Aug 12, 2010 5:23 am
santoostar wrote:Suppose we had the statement 1 andd 2 read

1. There are twice as many chocolate flavored cookies as there are almond flavored cookies in the jar.

2- One fifth of the cookies in the jar are almond flavored.

then, will the answer still be C?

My understanding says it would be E - correct me if i am wrong...( sorry if confused any1)..

Santo

no, the answer would still be (c). in fact, this was exactly the point of my illustration above with 1/7 and 2/7; if you didn't read that part of my post, go back and check it out.

with your numbers here, if you have both of those statements together, the fraction of chocolate cookies in the jar is 2 x 1/5 = 2/5. sufficient.
in your instance, the jar contains 1/5 almond, 2/5 chocolate, and 2/5 mystery cookies that you have no idea what they are -- but you don't care. all you care about is the fraction of cookies that are chocolate, and you have that fraction.
Ron has been teaching various standardized tests for 20 years.

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by santoostar » Thu Aug 12, 2010 7:12 am
lunarpower wrote:
santoostar wrote:Suppose we had the statement 1 andd 2 read

1. There are twice as many chocolate flavored cookies as there are almond flavored cookies in the jar.

2- One fifth of the cookies in the jar are almond flavored.

then, will the answer still be C?

My understanding says it would be E - correct me if i am wrong...( sorry if confused any1)..

Santo

no, the answer would still be (c). in fact, this was exactly the point of my illustration above with 1/7 and 2/7; if you didn't read that part of my post, go back and check it out.

with your numbers here, if you have both of those statements together, the fraction of chocolate cookies in the jar is 2 x 1/5 = 2/5. sufficient.
in your instance, the jar contains 1/5 almond, 2/5 chocolate, and 2/5 mystery cookies that you have no idea what they are -- but you don't care. all you care about is the fraction of cookies that are chocolate, and you have that fraction.
well..i see it now.....i was just concentrating on the total - thinking that would make a difference...thanks for helping me understand....

santo
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