Tag: math & puzzles

To find the conditional probability of event A given event B has occurred, we can use the formula for conditional probability:

[ P(A|B) = \frac{P(A \cap B)}{P(B)} ]

Given that the joint probability of events A and B is 32%, we have ( P(A \cap B) = 32\% = 0.32 ).

Given that the probability of event A is 60%, we have ( P(A) = 60\% = 0.60 ).

Given that the probability of event B is 50%, we have ( P(B) = 50\% = 0.50 ).

Substituting these values into the formula for conditional probability, we have:

[ P(A|B) = \frac{0.32}{0.50} \approx 0.64 ]

Therefore, the conditional probability of event A given event B has occurred is closest to 64.0%. Hence, the correct answer is option C.

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To answer this question, we need to understand the concept of the cash conversion cycle (CCC). The CCC measures the time it takes for a company to convert its resources into cash flow. It is calculated by adding the number of days of inventory and the number of days of receivables and subtracting the number of days of payables.

Given: Number of days of receivables: 48 Number of days of inventory: 37 Number of days of payables: 28

To calculate the cash conversion cycle (CCC), we use the following formula:

CCC = Number of days of inventory + Number of days of receivables - Number of days of payables

Substituting the given values, we get:

CCC = 37 + 48 - 28 CCC = 57

Therefore, the cash conversion cycle for the company is closest to 57 days.

The correct answer is A.

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To determine the expected growth rate of Company 1 compared to Company 2, we need to consider the given information about dividend payout ratio, return on assets, and financial leverage.

The growth rate of a company can be estimated using the sustainable growth rate (SGR) formula:

SGR = (Return on Assets) × (1 - Dividend Payout Ratio) × (Financial Leverage)

Let's calculate the SGR for Company 1 and Company 2:

SGR1 = (12%)(1 - 37.5%)(1.6) = 7.2% SGR2 = (10.0%)(1 - 40.0%)(2.0) = 12.0%

Comparing the SGRs, we can see that the SGR for Company 1 is 7.2%, and the SGR for Company 2 is 12.0%.

Since the SGR for Company 1 is lower than the SGR for Company 2, we can conclude that the expected growth rate of Company 1 is lower than that of Company 2.

Therefore, the correct answer is A) lower.

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To answer this question, we need to understand the differences between long investment time horizons and short investment time horizons.

Investors with long investment time horizons typically have more time to ride out market fluctuations and are generally more focused on long-term growth. They can afford to have their funds tied up in investments for longer periods and may prioritize capital appreciation over immediate liquidity.

On the other hand, investors with short investment time horizons have less time to recover from potential losses and may need access to their funds quickly. They are typically more concerned with preserving capital and may prioritize liquidity over potential long-term growth.

With this understanding, let's go through each option to determine the most likely requirement for investors with short investment time horizons:

Option A) Less liquidity and less emphasis on capital appreciation - This option is incorrect because investors with short investment time horizons generally require more liquidity, not less.

Option B) More liquidity and less emphasis on capital appreciation - This option is correct because investors with short investment time horizons typically need more liquidity and are less focused on capital appreciation.

Option C) Less liquidity and greater emphasis on capital appreciation - This option is incorrect because investors with short investment time horizons generally require more liquidity, not less, and are less focused on capital appreciation.

Option D) None of the above - This option is incorrect because option B is the correct answer.

Therefore, the correct answer is B) more liquidity and less emphasis on capital appreciation. This option aligns with the requirements of investors with short investment time horizons.

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To answer this question, let's go through each option to understand why it is correct or incorrect:

Option A) The optimal portfolio for an investor is the portfolio that lies on the efficient frontier and provides her with the greatest level of utility.

This option is correct. The efficient frontier represents a set of portfolios that offer the highest expected return for a given level of risk. The optimal portfolio for an investor is the one that maximizes their utility (satisfaction) based on their risk and return preferences. Therefore, this statement is likely to be correct.

Option B) The optimal portfolio for an investor is found at the point of tangency between the efficient frontier and an investor’s highest utility curve.

This option is correct. The point of tangency between the efficient frontier and an investor's highest utility curve represents the optimal portfolio for that investor. This is where the investor's risk and return preferences align with the available investment opportunities on the efficient frontier.

Option C) A more risk-averse investor will lie inside the efficient frontier but will lie outside the efficient frontier for a less risk-averse investor.

This option is incorrect. A more risk-averse investor will actually lie on a lower portion of the efficient frontier, where portfolios have lower expected returns but also lower levels of risk. A less risk-averse investor will lie on a higher portion of the efficient frontier, where portfolios have higher expected returns but also higher levels of risk. Therefore, this statement is least likely to be correct.

Option D) None of the above.

This option is incorrect because option C is least likely to be correct.

The correct answer is C. This option is least likely to be correct because it incorrectly states that a more risk-averse investor will lie inside the efficient frontier but will lie outside the efficient frontier for a less risk-averse investor.

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To answer this question, we need to understand the primary motivations for investment in commodities.

Option A) Positive correlation of commodities with unexpected inflation - This option is correct because commodities have a positive correlation with unexpected inflation. When inflation occurs unexpectedly, the prices of commodities tend to rise. Investors may invest in commodities to protect their purchasing power and hedge against inflation.

Option B) Positive correlation of commodities with stock and bond investments - This option is incorrect. While commodities may have some correlation with stock and bond investments, it is not their primary motivation for investment.

Option C) Positive volatility of commodities relative to stock and bond investments - This option is incorrect. While commodities may have higher volatility compared to stock and bond investments, it is not their primary motivation for investment.

Option D) None of the above - This option is incorrect. The correct answer is option A, as explained above.

The correct answer is option A) positive correlation of commodities with unexpected inflation. This option is correct because commodities are often seen as a hedge against inflation and tend to perform well during periods of unexpected inflation.

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To answer this question, we can analyze the given statements:

1. Tanya is older than Eric.
2. Cliff is older than Tanya.
3. Eric is older than Cliff.

Let's consider the implications of these statements:

If Tanya is older than Eric, and Cliff is older than Tanya, then it follows that Cliff is older than Eric. This contradicts the third statement which states that Eric is older than Cliff.

Therefore, since the third statement contradicts the first two statements, the correct answer is B) False.

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