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Intern  Joined: 28 Dec 2014
Posts: 1
What is the probability of selecting a white ball from a jar?  [#permalink]

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7 00:00

Difficulty:   95% (hard)

Question Stats: 25% (01:42) correct 75% (01:22) wrong based on 268 sessions

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What is the probability of selecting a white ball from a jar?

(1) There are twice as many white balls as balls of any other color
(2) There are 30 more white balls than balls of any other colors combined
Manager  Joined: 22 Oct 2014
Posts: 88
Concentration: General Management, Sustainability
GMAT 1: 770 Q50 V45 GPA: 3.8
WE: General Management (Consulting)
Re: What is the probability of selecting a white ball from a jar?  [#permalink]

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4
1

Question Stem: The stem does not provide much information, only that there is a Jar with white balls in it (probably more colors as well) and we are asked to determine whether we have enough information to calculate the probability of selecting a white ball. To calculate the probability we therefore need to know the ratio of white balls to balls of any other color.

Statement 1: We learn that there are twice as many white balls as balls of any other color. This is insufficient, as we don't know how many other colors are there. We might for example have 10 white balls and 5 red balls, which would give a ratio of 10:5 and a probability of $$\frac{10}{(10+5)}=\frac{10}{15}=\frac{2}{3}$$. We might also have 10 white balls, 5 red balls and 5 blue balls, which leads to 10:5:5 and $$\frac{10}{(10+5+5)}=\frac{1}{2}$$.

Statement 2: This is also insufficient, as we only know about absolute values, not about ratios. There could be for example 40 white balls and 10 red balls. This leads to 4:1 or $$\frac{40}{(40+10)}=\frac{4}{5}$$. Or we have 90 white balls and 60 red balls, which leads to $$\frac{90}{(90+60)}=\frac{4}{5}$$.

Combined: This is sufficient. If we have twice as many white balls as balls of any other color and 30 white balls more than all other balls combined, these two statements contradict each other for more than 1 other color: If there are two other colors, red and blue, and we have double the amount of white balls, the sum of red and blue balls must equal the number of white balls, which contradicts statement 2. We can therefore conclude that there is only 1 other color and the two equations:

$$number of white balls = 2 * number of red balls$$
$$number of white balls = 30 + number of red balls$$.

If you don't see the answer directly, you can plug one equation into the other and get 60 white balls and 30 red balls. From that we can derive the probability of selecting a white ball: $$\frac{60}{(60+30)}=\frac{2}{3}$$. Answer C is sufficient.
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Intern  Joined: 16 Jan 2015
Posts: 2
Re: What is the probability of selecting a white ball from a jar?  [#permalink]

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There is a 100% probability. The balls are in a jar. Jars are made of glass
Manager  Joined: 22 Oct 2014
Posts: 88
Concentration: General Management, Sustainability
GMAT 1: 770 Q50 V45 GPA: 3.8
WE: General Management (Consulting)
Re: What is the probability of selecting a white ball from a jar?  [#permalink]

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Don't assume the purpose of the one selecting the ball is selecting a white ball... _________________
$$\sqrt{-1}$$ $$2^3$$ $$\Sigma$$ $$\pi$$ ... and it was delicious!

Please consider giving +1 Kudos if deserved!
Intern  B
Joined: 21 Nov 2016
Posts: 41
Re: What is the probability of selecting a white ball from a jar?  [#permalink]

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bumpbot wrote:
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

Hi Bunnuel,

This is similar to the post that you had replied https://gmatclub.com/forum/if-a-pencil- ... 74394.html I totally agree with your answer for the post in this link. However, this similar question seems to have a different OA. I felt A would be enough if we were to solve this based on the explanation in the other question in the link.
Kindly let me know if I am right ? Or if the OA is right and I am making a mistake in analyzing the question.

Regards,
Kishore
Retired Moderator P
Joined: 22 Aug 2013
Posts: 1438
Location: India
Re: What is the probability of selecting a white ball from a jar?  [#permalink]

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reachskishore wrote:
bumpbot wrote:
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

Hi Bunnuel,

This is similar to the post that you had replied https://gmatclub.com/forum/if-a-pencil- ... 74394.html I totally agree with your answer for the post in this link. However, this similar question seems to have a different OA. I felt A would be enough if we were to solve this based on the explanation in the other question in the link.
Kindly let me know if I am right ? Or if the OA is right and I am making a mistake in analyzing the question.

Regards,
Kishore

Hi

The question that you have linked to is very similar to this question. But the first statement of this white ball question is slightly different from second statement of the linked pencil question. Lets write them down:

Statement 1, white ball question: There are twice as many white balls as balls of any other colour.

So if the jar has only white and red balls, then if number of red balls is 'x', number of white balls is '2x'. And required probability of drawing a white ball = 2x/(2x+x) = 2/3
But if jar has white and red and blue balls, then if number of white balls = 2x, then no of red = no of blue = x each (twice as many white balls as balls of any other color)
In this case required probability = 2x/(2x+x+x) = 1/2

Answers can be different you see. So Insufficient.

Statement 2, pencil question: There are 3 times as many red pencils as pencils of ALL other colors combined.

If you read carefully, this statement is different. It says no matter how many coloured pencils are there, if all other coloured pencils be 'x' in number combined, then number of red pencils = '3x'. So the ratio of red and non-red pencils will Always be 3:1 (unlike white ball question)..

So required probability in that case = 3/4 always.. Sufficient.

Hope this helps.
Intern  B
Joined: 29 May 2018
Posts: 4
Re: What is the probability of selecting a white ball from a jar?  [#permalink]

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Hi Bunuel,

Can you please help over here, I believe the answer is E since, we do not know how many other colour balls are there.
Intern  B
Joined: 05 Aug 2018
Posts: 18
GMAT 1: 650 Q46 V34 Re: What is the probability of selecting a white ball from a jar?  [#permalink]

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skydive wrote:
What is the probability of selecting a white ball from a jar?

(1) There are twice as many white balls as balls of any other color
(2) There are 30 more white balls than balls of any other colors combined

This is a very good question. However, there is 1 error in the question stem:

Answer choice (2) should be stated as follows: "There are 30 more white balls than balls of all other colors combined." Re: What is the probability of selecting a white ball from a jar?   [#permalink] 27 Jan 2019, 03:32
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