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Containers A and B each contain 8 gold coins, 12 silver coins, and not

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Containers A and B each contain 8 gold coins, 12 silver coins, and not [#permalink]

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New post 29 Jul 2017, 00:58
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Containers A and B each contain 8 gold coins, 12 silver coins, and nothing else. Container C contains 1 gold coin, 4 silver coins, and nothing else. A container is chosen at random and then a coin is chosen at random from that container. What is the probability that the chosen coin is silver?


A. 4/15

B. 2/5

C. 7/15

D. 3/5

E. 2/3
[Reveal] Spoiler: OA

Last edited by chetan2u on 29 Jul 2017, 05:22, edited 2 times in total.
updated the OA
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Re: Containers A and B each contain 8 gold coins, 12 silver coins, and not [#permalink]

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New post 29 Jul 2017, 01:02
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Is this approach correct?


(1/3 x 0/8) + (1/3 x 12/20) + (1/3 x 4/5) = 7/15


i.e. Prob of selecting that box X Probability of getting a silver in that box


summation of this for all 3 boxes
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Re: Containers A and B each contain 8 gold coins, 12 silver coins, and not [#permalink]

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New post 29 Jul 2017, 01:15
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Does anyone think the question is quite misleading? Containers A and B "each" contains 8 gold coins, 12 silver coins, and nothing else. Does this not indicate that A contains 8G and 12S and that B contains the same coins as A? Only after I finish my calculation that I realized this way was wrong.
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Re: Containers A and B each contain 8 gold coins, 12 silver coins, and not [#permalink]

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New post 29 Jul 2017, 01:38
3newton wrote:
Is this approach correct?


(1/3 x 0/8) + (1/3 x 12/20) + (1/3 x 4/5) = 7/15


i.e. Prob of selecting that box X Probability of getting a silver in that box


summation of this for all 3 boxes

Hey 3newton,
Can you please tell why you have multiplied 0/3. Rest of he things are clear.
Tanks in advance.

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Re: Containers A and B each contain 8 gold coins, 12 silver coins, and not [#permalink]

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New post 29 Jul 2017, 01:39
Rather I would have gone for 1/3(12/20+12/20+4/5).
Thus would have led to 2/3.
Ans E.

Please correct my understanding of needed.

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Re: Containers A and B each contain 8 gold coins, 12 silver coins, and not [#permalink]

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New post 29 Jul 2017, 05:06
kumarparitosh123 wrote:
Rather I would have gone for 1/3(12/20+12/20+4/5).
Thus would have led to 2/3.
Ans E.

Please correct my understanding of needed.

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The line "Containers A and B each contain 8 gold coins, 12 silver coins, and nothing else" is quite misleading here.
What it actually wants to say is that Container A contains 8 Gold coins and nothing else, and Container B contains 12 Silver coins and nothing else.

Seems to be a poor quality question..
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Re: Containers A and B each contain 8 gold coins, 12 silver coins, and not [#permalink]

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New post 29 Jul 2017, 05:21
3newton wrote:
Containers A and B each contain 8 gold coins, 12 silver coins, and nothing else. Container C contains 1 gold coin, 4 silver coins, and nothing else. A container is chosen at random and then a coin is chosen at random from that container. What is the probability that the chosen coin is silver?


A. 4/15

B. 2/5

C. 7/15

D. 3/5

E. 2/3



Hi...
the way Q is written, answer is clearly E.....

Q means BOTH A and B contain 8G and 12S. container C contains 1G and 4S..

Now how have you interpreted it as 0 silver in A is wrong...

Any of three can be choosen, so choosing each means probability of 1/3..

total \(\frac{1}{3}*\frac{12}{20}*2+\frac{1}{3}*\frac{4}{5} = \frac{2}{3}\)

E
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Containers A and B each contain 8 gold coins, 12 silver coins, and not [#permalink]

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New post 29 Jul 2017, 05:22
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3newton wrote
Quote:
Containers A and B each contain 8 gold coins, 12 silver coins, and nothing else. Container C contains 1 gold coin, 4 silver coins, and nothing else. A container is chosen at random and then a coin is chosen at random from that container. What is the probability that the chosen coin is silver?

A. 4/15

B. 2/5

C. 7/15

D. 3/5

E. 2/3

K_Leon wrote:
Does anyone think the question is quite misleading? Containers A and B "each" contains 8 gold coins, 12 silver coins, and nothing else. Does this not indicate that A contains 8G and 12S and that B contains the same coins as A? Only after I finish my calculation that I realized this way was wrong.

Yes. I remain confused. I got the correct answer through no fault of my own. I guessed.

A thorough discussion of "each" and "both" belongs in SC, so I'll keep it as short as I can. One hat I wear is editor of English prose.

"Each" refers to every one of any number, when considered individually or separately. "Both" refers to two, taken together. "Each," almost always, is a singular subject (hence singular verb). "Both" is a plural subject. The prompt's plural verb "contain" implies both. ????

"Each" should be used to emphasize the individuality of separate conditions. "The company gave both women $100,000." Unclear. Corrected: "The company gave each woman $100,000." (The women did not split the $100,000.)

Clarity would be simple to achieve. "Jars A and B both contain ..." Or "Jars A and B contain, respectively, 8 gold and 12 silver coins."

I still can't figure out how, in 3newton 's response, A has 0 silver coins of 8 total but B has 12 silver coins of 20 total. Doesn't A also have 20 coins?

If A = 8 total and B = 12 total, I think the equation is (1/3 * 0/8) + (1/3 * 12/12) + (1/3 * 4/5) = 3/5

kumarparitosh123 , I think you are correct.

If A and B both have 8 gold and 12 silver coins, I agree that the equation is (1/3 * 12/20) + (1/3 * 12/20) + (1/3 * 4/5) = 2/3

That said, if words were clear and OA were different, the content would be interesting. 3newton , are you sure the OA is correct?

chetan2u , I disagree respectfully. I don't think there's anything clear about it. Both answers D and E are defensible.
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Containers A and B each contain 8 gold coins, 12 silver coins, and not [#permalink]

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New post 29 Jul 2017, 05:33
genxer123 wrote:
3newton wrote
Quote:
Containers A and B each contain 8 gold coins, 12 silver coins, and nothing else. Container C contains 1 gold coin, 4 silver coins, and nothing else. A container is chosen at random and then a coin is chosen at random from that container. What is the probability that the chosen coin is silver?

A. 4/15

B. 2/5

C. 7/15

D. 3/5

E. 2/3

K_Leon wrote:
Does anyone think the question is quite misleading? Containers A and B "each" contains 8 gold coins, 12 silver coins, and nothing else. Does this not indicate that A contains 8G and 12S and that B contains the same coins as A? Only after I finish my calculation that I realized this way was wrong.

Yes. I remain confused. I got the correct answer through no fault of my own. I guessed.

A thorough discussion of "each" and "both" belongs in SC, so I'll keep it as short as I can. One hat I wear is editor of English prose.

"Each" refers to every one of any number, when considered individually or separately. "Both" refers to two, taken together. "Each," almost always, is a singular subject (hence singular verb). "Both" is a plural subject. The prompt's plural verb "contain" implies both. ????

"Each" should be used to emphasize the individuality of separate conditions. "The company gave both women $100,000." Unclear. Corrected: "The company gave each woman $100,000." (The women did not split the $100,000.)

Clarity would be simple to achieve. "Jars A and B both contain ..." Or "Jars A and B contain, respectively, 8 gold and 12 silver coins."

I still can't figure out how, in 3newton 's response, A has 0 silver coins of 8 total but B has 12 silver coins of 20 total. Doesn't A also have 20 coins?

If A = 8 total and B = 12 total, I think the equation is (1/3 * 0/8) + (1/3 * 12/12) + (1/3 * 4/5) = 3/5

kumarparitosh123 , I think you are correct.

If A and B both have 8 gold and 12 silver coins, I agree that the equation is (1/3 * 12/20) + (1/3 * 12/20) + (1/3 * 4/5) = 2/3

That said, if words were clear and OA were different, the content would be interesting. 3newton , are you sure the OA is correct?

chetan2u ,I disagree respectfully. I don't think there's anything clear about it. Both answers D and E are defensible.


Hi,

Disagreement is always good, and with respect is even better :wink: .
So I may agree with what you have written but not with D as answer in any way, neither mathematically or grammatically..

an error of contain/contains is perfectly fine in the forum, may not be in actuals. but there too it would mean the same.

say if I take what you say --
Quote:
Containers A and B each contain 8 gold coins, 12 silver coins, and nothing else. could mean the equation is (1/3 * 0/8) + (1/3 * 12/12) + (1/3 * 4/5) = 3/5

so A has 8 gold coins , B has 12 silver BUT WHO has " nothing else"
so this solution does not stand grammatically too..
E is the only possible answer.
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Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html


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Containers A and B each contain 8 gold coins, 12 silver coins, and not [#permalink]

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New post 29 Jul 2017, 07:21
chetan2u wrote:
genxer123 wrote:

chetan2u ,I disagree respectfully. I don't think there's anything clear about it. Both answers D and E are defensible.


Hi,

Disagreement is always good, and with respect is even better :wink: .
So I may agree with what you have written but not with D as answer in any way, neither mathematically or grammatically..

an error of contain/contains is perfectly fine in the forum, may not be in actuals. but there too it would mean the same.

say if I take what you say --
Quote:
Containers A and B each contain 8 gold coins, 12 silver coins, and nothing else. could mean the equation is (1/3 * 0/8) + (1/3 * 12/12) + (1/3 * 4/5) = 3/5

so A has 8 gold coins , B has 12 silver BUT WHO has " nothing else"
so this solution does not stand grammatically too..
E is the only possible answer.


"A has 8 gold coins, B has 12 silver coins, and [in each there is] nothing else."

That's correct, grammatically.
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Re: Containers A and B each contain 8 gold coins, 12 silver coins, and not [#permalink]

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New post 28 Aug 2017, 23:20
I did a more 'one at a time' probability and added them up:
--> prob of container: 1/3 (choosing one out of 3 containers A,B,C)
--> prob of silver per container --> if either A and B --> then 1/12
--> if either C --> then 1/4
Prob of all silver --> 1/4 + 1/16 = 1/3
--> Prob of silver and container =1/3 + 1/3 -->2/3 (E)
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Re: Containers A and B each contain 8 gold coins, 12 silver coins, and not [#permalink]

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New post 28 Aug 2017, 23:24
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Also, I do notice an error in phrasing 'each contain' -- since I read container A and B; it skipped my attention. (this is not advisable anyway in GMAT exam where every word is important) . Now it would complicate matters because it means A and B total would be 16 gold and 24 silver coins --> I think this question needs to be re-phrased :)
Re: Containers A and B each contain 8 gold coins, 12 silver coins, and not   [#permalink] 28 Aug 2017, 23:24
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