Question

Direction: A few statements have been given in each of the following questions. Analyse the given statements and answer whether the data given in the statements is sufficient to answer the question or not.
A box contains 20 tops of the same size and pattern. Each top is either white, black, or grey in colour. Find the number of black tops in the box.
Statement I: The probability of picking a black top is the same as the probability of picking a grey top.
Statement II: The number of grey tops is more than that of white tops.
Statement III: The probability of picking a white top is 20%.

• A. If the data in Statement I alone is sufficient.
• B. If data in all Statements I, II, and III is sufficient.
• C. If the data in only Statements I and III are sufficient.
• D. If the data in only Statement III is sufficient.
• E. If the data in all Statements I, II, and III are not sufficient.

Answer 1

The Correct Option is C

Let the number of white, black, and grey tops in the box be \(x, y\), and \(z\), respectively.

From Statement I:

\(\frac{^yC1}{^{20}C1} = \frac{^zC1}{^{20}C1}\)

\(⇒ y = z\)

Not Sufficient

From Statement II:
\(z > x\)
Not Sufficient

From Statement III:
The probability of picking a white top = \(\frac{^xC1}{^{20}C1} = \frac{20}{100}\)

\(⇒ \frac{x}{20} = \frac{1}{5}\)

\(⇒ x = 4\)

Not Sufficient
If we combine the statements I and III together,
We have \(x = 4\) and total number of tops = \(20\), so the sum of number of black and grey tops = \(16\)
As the probability of both picking up is same, so \(y = z = 8\)
Hence, the data in statements I and III together is sufficient.

Hence, option C is the correct answer.