Tag: math & puzzles

Questions Related to math & puzzles

The joint probability of events A and B is 32 percent with the probability of event A being 60 percent and the probability of event B being 50 percent. Based on this information, the conditional probability of event A given event B has occurred is closest to:

general knowledge math & puzzles

  1. 30.0%.

  2. 53.3%

  3. 64.0%

  4. 16.0%

Show answer
Correct Option: C

AI Explanation

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.

An analyst has calculated the following ratios for a company: Number of days of receivables 48 Number of days of inventory 37 Number of days of payables 28 The cash conversion cycle for the company is closest to:
general knowledge math & puzzles

  1. 57 days

  2. 85 days

  3. 113 days

  4. 65

Show answer
Correct Option: A

An analyst gathers the following information about two companies for the year ending 31 December 2008: Company 1 Company 2 Dividend payout ratio 37.5% 40.0% Return on assets 12% 10.0% Financial leverage 1.6 2.0 Which of the following best describes the expected growth rate of Company 1? The expected growth rate of Company 1 compared to Company 2 is
general knowledge math & puzzles

  1. lower.

  2. greater.

  3. the same

  4. none of the above

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Correct Option: C

An investor purchases a 1-month out-of-the-money American call option on a stock. A week later, the stock price is less than the call option strike price. The time value of the option is most likely:

general knowledge math & puzzles

  1. Zero.

  2. A positive amount.

  3. A negative amount

  4. none of the above

Show answer
Correct Option: B

Compared to investors with long investment time horizons, investors with short investment time horizons most likely require:

general knowledge math & puzzles

  1. less liquidity and less emphasis on capital appreciation

  2. more liquidity and less emphasis on capital appreciation.

  3. less liquidity and greater emphasis on capital appreciation

  4. none of the above

Show answer
Correct Option: B

AI Explanation

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.

Which of the following statements regarding the Markowitz efficient frontier is least likely to be correct? The optimal portfolio for:
general knowledge math & puzzles

  1. an investor is the portfolio that lies on the efficient frontier and provides her with the greatest level of utility.

  2. an investor is found at the point of tangency between the efficient frontier and an investor’s highest utility curve.

  3. a more risk-averse investor will lie inside the efficient frontier but will lie outside the efficient frontier for a less risk-averse investor.

  4. none of the above

Show answer
Correct Option: C

A primary motivation for investment in commodities is most likely the:
general knowledge math & puzzles

  1. positive correlation of commodities with unexpected inflation

  2. positive correlation of commodities with stock and bond investments.

  3. positive volatility of commodities relative to stock and bond investments

  4. none of the above

Show answer
Correct Option: A

An analyst is developing net present value (NPV) profiles for two investment projects. The only difference between the two projects is that Project 1 is expected to receive larger cash flows early in the life of the project, while Project 2 is expected to receive larger cash flows late in the life of the project. The slope of the NPV profile for Project 1 when compared to the slope of the NPV profile for Project 2 is most likely:

general knowledge math & puzzles

  1. equal.

  2. flatter

  3. steeper

  4. unequal

Show answer
Correct Option: B

There are three cans A, B and C. The capacities of A, B and C are 6 litres, 10 litres and 16 litres respectively. The can C contains 16 litres of milk. The milk has to be divided in them using these three cans only. Consider the following statements : 1. It is possible to have 6 litres of milk each in can A and can B. 2. It is possible to have 8 litres of milk each in can B and can

general knowledge math & puzzles

  1. 1

  2. 2

  3. Both 1 and 2

  4. None of Them

Show answer
Correct Option: C
Explanation:

To solve this problem, the user needs to know the capacities of each can and how to divide the milk among the cans to obtain the desired quantities.

Statement 1: It is possible to have 6 litres of milk each in can A and can B. To obtain 6 litres of milk in can A and can B, we can follow the following steps:

  • Pour 6 litres of milk from can C into can A.
  • Pour 4 litres of milk from can A into can B.
  • Pour 2 litres of milk from can C into can A.
  • Pour 4 litres of milk from can A into can B.

After following these steps, can A will have 4 litres of milk, can B will have 6 litres of milk, and can C will have 10 litres of milk. Therefore, statement 1 is true.

Statement 2: It is possible to have 8 litres of milk each in can B and can A. To obtain 8 litres of milk in can A and can B, we can follow the following steps:

  • Pour 10 litres of milk from can C into can B.
  • Pour 2 litres of milk from can B into can A.
  • Pour 4 litres of milk from can C into can B.
  • Pour 2 litres of milk from can B into can A.

After following these steps, can A will have 4 litres of milk, can B will have 8 litres of milk, and can C will have 12 litres of milk. Therefore, statement 2 is true.

Since both statements are true, the answer is:

The Answer is: C. Both 1 and 2.

Tanya is older than Eric. Cliff is older than Tanya. Eric is older than Cliff. If the first two statements are true, the third statement is
general knowledge math & puzzles

  1. True

  2. False

  3. Uncertain

  4. None

Show answer
Correct Option: B