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# A bag contains a total of 20 only red and white marbles, fewer than

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Intern
Joined: 22 Feb 2018
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A bag contains a total of 20 only red and white marbles, fewer than  [#permalink]

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10 Oct 2018, 02:58
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Difficulty:

75% (hard)

Question Stats:

51% (02:18) correct 49% (02:38) wrong based on 66 sessions

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A bag contains a total of 20 only red and white marbles, fewer than half of which are red. Two marbles are to be drawn simultaneously from the bag. How many marbles in bag are red?

(1) The probability that the two marbles to be drawn will be red is 1/19.
(2) The probability that one marble to be drawn will be red and the other will be white is 15/19.
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Re: A bag contains a total of 20 only red and white marbles, fewer than  [#permalink]

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10 Oct 2018, 03:10
jpfg259 wrote:
A bag contains a total of 20 only red and white marbles, fewer than half of which are red. Two marbles are to be drawn simultaneously from the bag. How many marbles in bag are red?

(1) The probability that the two marbles to be drawn will be red is 1/19.
(2) The probability that one marble to be drawn will be red and the other will be white is 15/19.

Question: Number of Red marbles = ?

Given: R+W = 20
R < 10

Statement 1: The probability that the two marbles to be drawn will be red is 1/19.

$$(R/20)*[(R-1)/19] = 1/19$$

i.e. $$R*(R-1) = 20$$
i.e. $$R = 5$$ (As R can Not be -5)

SUFFICIENT

Statement 2: The probability that one marble to be drawn will be red and the other will be white is 15/19

$$(R/20)*(W/19)*2! = 15/19$$

i.e. $$R*W = 150$$
and $$R+W = 20$$
There seems flaw in second statement however with correct probability this statement will be proven Sufficient

SUFFICIENT

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Joined: 22 Feb 2018
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Re: A bag contains a total of 20 only red and white marbles, fewer than  [#permalink]

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10 Oct 2018, 04:39
Hi, thank you for your help! Quick question concerning statement 1, when you said
Quote:
R=5 (As R can Not be -5)
, did you mean "As R cannot be -4"?

If I solve the equation for R(R-1) = 20, I get the following:
$$R^2-R-20=0$$
(R+4) (R-5) = 0
R = -4 or 5
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Re: A bag contains a total of 20 only red and white marbles, fewer than  [#permalink]

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10 Oct 2018, 06:41
jpfg259 wrote:
Hi, thank you for your help! Quick question concerning statement 1, when you said
Quote:
R=5 (As R can Not be -5)
, did you mean "As R cannot be -4"?

If I solve the equation for R(R-1) = 20, I get the following:
$$R^2-R-20=0$$
(R+4) (R-5) = 0
R = -4 or 5

jpfg259

YES, you are absolutely correct in inferring what I meant in my statement.

However, I wish to add that I do NOT get into quadratic equation forming till I can solve the expression using my logical ability with number picking.

You can also try that to believe that It saves a lot of time and energy that you may other waste in making and then simplifying a quadratic expressions.

A very useful way to solve many questions in Work rate as well.

I hope this helps!!!
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Intern
Joined: 22 Feb 2018
Posts: 10
A bag contains a total of 20 only red and white marbles, fewer than  [#permalink]

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Updated on: 10 Oct 2018, 13:56
I am not sure what you meant by "I wish to add that I do NOT get into quadratic equation forming till I can solve the expression using my logical ability with number picking".

Additionally, you mentioned "there seems flaw in second statement."
What is that flaw you are talking about?

Originally posted by jpfg259 on 10 Oct 2018, 13:16.
Last edited by jpfg259 on 10 Oct 2018, 13:56, edited 2 times in total.
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Re: A bag contains a total of 20 only red and white marbles, fewer than  [#permalink]

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10 Oct 2018, 13:40
1
jpfg259 wrote:
A bag contains a total of 20 only red and white marbles, fewer than half of which are red. Two marbles are to be drawn simultaneously from the bag. How many marbles in bag are red?

(1) The probability that the two marbles to be drawn will be red is 1/19.
(2) The probability that one marble to be drawn will be red and the other will be white is 15/19.

Let red marbles be x
White marbles be y

x + y = 20

We don’t know how much is x but we know it is less than 10

x could be 9,8,7,6,5 etc..

We are given a probability of 2 red marbles to be 1/19

This is a unique value and without any inputs it is enough to know how many red marbles. This sufficient, however for the sake of explaining how it is sufficient.

It is in this form (x/20)*(x-1)/19 = 1/19

It then becomes x^2 - x - 20 = 0
(x-5) (x+4) we know x cannot be negative so x = 5.

Sufficient.

We are given x/20 * y/19 = 15/19

x * y * 2 = 300
x * y = 150

x * (20 - x) = 150

20x - x^2 = 150

x^2 - 20x + 150 = 0

Here it seems something is off because the sum of roots = 20 however the product of the roots is 150 which is not possible.

However, as GMATinsight mentioned something must be adjusted for it to give a sufficient answer.

Posted from my mobile device
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Re: A bag contains a total of 20 only red and white marbles, fewer than  [#permalink]

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10 Oct 2018, 19:09
jpfg259 wrote:
I am not sure what you meant by "I wish to add that I do NOT get into quadratic equation forming till I can solve the expression using my logical ability with number picking".

Additionally, you mentioned "there seems flaw in second statement."
What is that flaw you are talking about?

The flaw is 1st statement and 2nd statement are not giving same values of R and W which doesn't happen in any GMAT standard question.

It's Impossible for the answers to contradicts between first and second statement OR between statement and question stem and that's why the question is flawed.
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Intern
Joined: 22 Feb 2018
Posts: 10
Re: A bag contains a total of 20 only red and white marbles, fewer than  [#permalink]

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17 Oct 2018, 02:03
Thank you GMATinsight Salsanousi for all the help!
Re: A bag contains a total of 20 only red and white marbles, fewer than   [#permalink] 17 Oct 2018, 02:03
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