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M09-11

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Bunuel
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M09-11 [#permalink] New post   16 Sep 2014, 00:39
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64% (01:28) correct 36% (01:09) wrong based on 234 sessions
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A bowl contains only green and blue chips. If two chips are drawn from the bowl at random and without replacement, what is the probability that both chips will be blue?


(1) The ratio of blue chips to green chips in the bowl is 3:4.

(2) There are 5 more green chips in the bowl than blue chips.
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C
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Bunuel
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Re M09-11 [#permalink] New post   16 Sep 2014, 00:39
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A bowl contains only green and blue chips. If two chips are drawn from the bowl at random and without replacement, what is the probability that both chips will be blue?

(1) The ratio of blue chips to green chips in the bowl is 3:4.

If \(B=3\) and \(G=4\), then \(P=\frac{3}{7}*\frac{2}{6}\), but if \(B=6\) and \(G=8\), then \(P=\frac{6}{14}*\frac{5}{13}\). We get two different answers, so this information is not sufficient.

(2) There are 5 more green chips in the bowl than blue chips.

So, \(G=B+5\). This information is clearly insufficient by itself.

(1)+(2) Combining the information, we have \(B:G=3:4\) and \(G=B+5\). Solving this system of equations gives us: \(B=15\) and \(G=20\). With this information, we can find the probability: \(P=\frac{15}{35}*\frac{14}{34}\). Sufficient.


Answer: C
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Re: M09-11 [#permalink] New post   10 Oct 2017, 23:04
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This is how I approached this.

Given: Bowl contains only Blue and Green Chips. Replacement is not allowed. This is Value question and not yes/no

S1: Blue Chips : Green Chip = 3x : 4x

=> Probability of picking two blue =\(\frac{3x}{7x} * \frac{(3x-1)}{(7x-1)}\). This cannot be solved without knowing the value of x. Insufficient.

S2: Clearly insufficient. Blue and Green could be any number. The probability will be different for different cases.


S1+S2 : We have \(4x - 3x = 5 => x = 5\). Knowing x and using S1, we can now find the probablity. Hence sufficient.

Final answer: C
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Re: M09-11 [#permalink] New post   07 May 2018, 02:33
I think this is a high-quality question and I agree with explanation.
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Re: M09-11 [#permalink] New post   20 Jun 2018, 20:12
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I think this is a high-quality question and I agree with explanation.

Posted from my mobile device
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Re: M09-11 [#permalink] New post   25 Nov 2019, 05:47
hello Bunnel,

Can you please share the link of more similar problems.

Thanks
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Bunuel
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Re: M09-11 [#permalink] New post   25 Nov 2019, 05:54
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prabsahi06 wrote:
hello Bunnel,

Can you please share the link of more similar problems.

Thanks


Similar questions:
https://gmatclub.com/forum/a-box-contai ... fl=similar
https://gmatclub.com/forum/a-box-contai ... 44131.html
https://gmatclub.com/forum/initially-ho ... fl=similar
https://gmatclub.com/forum/if-a-barrel- ... fl=similar
https://gmatclub.com/forum/a-barrel-con ... fl=similar
https://gmatclub.com/forum/a-certain-bo ... fl=similar
https://gmatclub.com/forum/a-box-contai ... fl=similar
https://gmatclub.com/forum/a-box-contai ... fl=similar
https://gmatclub.com/forum/a-box-contai ... fl=similar
https://gmatclub.com/forum/a-bag-contai ... fl=similar
https://gmatclub.com/forum/a-box-contai ... fl=similar
https://gmatclub.com/forum/a-box-contai ... fl=similar
https://gmatclub.com/forum/a-box-contai ... fl=similar

Hope it helps.
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Re: M09-11 [#permalink] New post   22 Jun 2020, 07:32
I think this is a high-quality question and I agree with explanation.
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Re: M09-11 [#permalink] New post   09 Mar 2021, 04:16
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. I don't understand the explanation how did you arrive at B =6 and G=8
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Re: M09-11 [#permalink] New post   09 Mar 2021, 07:01
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Urennaa wrote:
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. I don't understand the explanation how did you arrive at B =6 and G=8


(1) says that The ratio of blue chips to green chips is 3:4. So, the blue and green chips respectively can be:
3 and 4;
6 and 8;
9 and 12;
12 and 16;
15 and 20;
18 and 24;
...

Basically the number of blue and green chips are 3x and 4x for positive integer x.

(2) says that There are 5 more green chips than blue chips.

When combining, as you can see, only 15 and 20 satisfy the conditions. So, the answer is C.
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Re: M09-11 [#permalink] New post   28 Aug 2021, 23:05
The best thing you can learn from this question is the probability will always vary if you are given ratio of two entities.
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Re: M09-11 [#permalink] New post   09 May 2023, 07:26
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
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Re: M09-11 [#permalink] New post   09 Aug 2023, 09:44
I think this is a high-quality question and I agree with explanation.
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Re: M09-11 [#permalink]
09 Aug 2023, 09:44
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