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