In a Garden 40% of the Flowers are Roses and Rest are Carnations GMAT Problem Solving

Question: In a garden 40% of the flowers are roses and rest are carnations. If 1/4 of the roses and 1/10 of carnations are red, what is the probability that a red flower selected at random is a rose?

  1. \(\frac{1}{17}\)
  2. \(\frac{5}{8 }\)
  3. \(\frac{2}{3}\)
  4. \(\frac{3}{4}\)
  5. \(\frac{7}{9}\)


Correct Answer
: B

Solution and Explanation
Approach Solution 1:

Given:

  • In a garden 40% of the flowers are roses and rest are carnations.
  • 1/4 of the roses and 1/10 of carnations are red

Find out:

  • what is the probability that a red flower selected at random is a rose

Let us consider the basic mathematical way to solve the problem.
Let there be 100 flowers in the garden.
40% of the flowers are roses
So, the number of roses = 40
From this, we can say that the number of carnations will be the remaining ones.
No. of carnations = 100-40 = 60

\(\frac{1}{4}\)th of roses are red => No. of Red Roses = \(\frac{1}{4}\)∗40 = 10

\(\frac{1}{10}\)th of carnations are red => No. of Red Carnations = \(\frac{1}{10}\)∗60 = 6

Hence, no. of red flowers = 10+6 = 16
Answer = No of Red Roses / No.of Redflowers

=\(\frac{10}{16}\)

=⅝

Hence, the correct answer is B.

Approach Solution 2:

Given:

  • In a garden 40% of the flowers are roses and rest are carnations.
  • \(\frac{1}{4}\) of the roses and \(\frac{1}{10}\) of carnations are red

Find out:

  • what is the probability that a red flower selected at random is a rose

P(rose) = \(\frac{2}{5}\)

P(carnation) = \(\frac{3}{5}\)

Considering the first:

\(\frac{1}{4}*\frac{2}{5}\)

= \(\frac{1}{10}\) of roses are red

Considering the second:

\(\frac{1}{10}*\frac{3}{5}\)

= \(\frac{3}{50}\) of carnations are red

P(red rose) = \(\frac{1}{10}/(\frac{1}{10}+\frac{3}{50})\)

= \((\frac{1}{10})/(\frac{8}{50})\)

= \(\frac{1}{10}*\frac{25}{4}\)

= \(\frac{25}{40}\)

=\(\frac{5}{8}\)

Approach Solution 3:

Let there be 100 flowers

40% are roses
So, No. of roses = 40
and, No. of carnations = 100-40 = 60

¼ of roses are red => No. of Red Roses = 1/4∗40= 10
110110of carnations are red => No. of Red Carnations = 1/10∗60= 6

Hence, no. of red flowers = 10+6 = 16
Ans = No.ofRedRoses/No.ofRedflowers= 10/16= 5/8

“In a garden 40% of the flowers are roses and rest are carnations.”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.


Suggested GMAT Problem Solving Questions

Fees Structure

CategoryState
General15556

In case of any inaccuracy, Notify Us! 

Comments


No Comments To Show