A Bag Contains 5 Red Balls And Some Blue Balls GMAT Problem Solving

Question - A bag contains 5 red balls and some blue balls. If the probability of drawing a blue ball is double that of a red ball, find the number of blue balls in the bag. What is the number of blue balls in the bag.

1. 10
2. 5
3. 20
4. 15
5. 12

‘A bag contains 5 red balls and some blue balls.' - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMATOfficial Guide 2020”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Solution and Explanation

Approach Solution 1:

It is asked What is The number of blue balls in the bag. Let us use the probability approach
Evaluating further –
Having said that,
Probability is calculated as the sum of all probable outcomes.
Given that the likelihood of drawing a blue ball is twice as likely as a red ball, as stated in the question, that
Probability of drawing the blue ball = 2 times the probability of drawing the red ball.
There are now 5 red balls.
Let x represent the number of blue balls.
Number of balls total = x + 5
Number of outcomes that can occur / Total number of outcomes = probability of drawing the red ball
= 5/(x + 5)
Probability of drawing the blue ball = number of toalt outcomes / total Number of outcomes
= x/(x + 5)
Given that drawing a blue ball has a twofold higher probability than a red ball
x/(x + 5) = 2 [5/(x + 5)]
x = 10
Therefore the number of blue balls = 10
The answer is A which is 10

Correct Answer: A

Approach Solution 2:

Explanation - There is another approach to answering this question
Here The number of blue balls is unknown. However, a correlation between the likelihood of drawing a blue ball and a red ball is shown. In order to solve, we apply this condition. Probability is the proportion of favourable events to all possible outcomes.
Let the number of blue balls be x.
Acc to Given data:
Red balls is given = 5
And according to question
The Probability of drawing blue ball = 2×probability of drawing red ball……… (1)
We know that
Probability = \(\frac{favourable number of outcomes}{total number of outcomes}\)
Total balls = x + 5
Probability of drawing blue ball = \(\frac{x}{x+5}\)
Probability of drawing red ball = \(\frac{5}{x+5}\)
Using equation 1
Probability of drawing blue ball = twice probability of drawing red ball
\(\frac{x}{x+5}\) = 2 * \(\frac{5}{x+5}\)
x = 10
The answer is A which is 10

Correct Answer: A

Approach Solution 3:

Let us consider there are x blue balls in the bag.
So, the total number of balls in the bag = 5 + x
Now, the probability of drawing a blue ball be x/5+x
And , the probability of drawing a red ball be 5/5+x
The probability of drawing a blue ball in the question is mentioned to be double that of a red ball,
that implies x/5+x=2×5/5+x⇒x/5+x=10/5+x
that implies x^2+5x=50+10x
that implies x^2−5x−50=0
that implies x=5±√25+(4×5)/2
that implies x=5±152
that implies x = 10 or -5.
So the number of blue balls cannot be negative.
⇒ x = 10
Therefore, there are 10 blue balls in the bag.

Correct Answer: A

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