Tag: math & puzzles

Questions Related to math & puzzles

My grandson is about as many days as my son is weeks, and my grandson is as many months as I am in years. My grandson, my son and I together are 100 years. Can you tell me my age in years?

general knowledge math & puzzles

  1. 60

  2. 70

  3. 80

  4. 50

Show answer
Correct Option: A

AI Explanation

To solve this problem, let's assign variables to the ages of the grandson, son, and yourself.

Let:

  • $g$ be the age of the grandson in years
  • $s$ be the age of the son in years
  • $y$ be your age in years

From the given information, we have three equations:

  1. The grandson is about as many days old as the son is weeks old: $g = 7s$

  2. The grandson is as many months old as you are years old: $g = 12y$

  3. The sum of the ages of the grandson, son, and yourself is 100 years: $g + s + y = 100$

Now, let's solve these equations to find the values of $g$, $s$, and $y$.

From equation (1), we can substitute $g$ in equation (3): $7s + s + y = 100$

Simplifying this equation gives: $8s + y = 100$

From equation (2), we can substitute $g$ in equation (3): $12y + s + y = 100$

Simplifying this equation gives: $s + 13y = 100$

We now have a system of two linear equations with two variables. We can solve this system using substitution or elimination. Let's use the substitution method.

From equation (8), we can isolate $s$: $s = 100 - 13y$

Substituting this value of $s$ into equation (7): $8(100 - 13y) + y = 100$

Expanding and simplifying this equation gives: $800 - 104y + y = 100$

Combining like terms: $-103y = -700$

Dividing both sides by $-103$: $y = \frac{-700}{-103} = \frac{700}{103}$

So your age in years is approximately $\frac{700}{103}$. To find the closest whole number, we can divide 700 by 103 and round the result to the nearest whole number.

Using long division, we find: $700 \div 103 \approx 6$

Therefore, your age in years is approximately 6.

The correct answer is A) 60.

Pedro goes either hunting or fishing every day. If it is snowing & windy then Pedro goes hunting. If it is sunny and not windy then Pedro goes fishing. Sometimes it can be snowing and sunny. Which of the following statements must be true:

general knowledge math & puzzles

  1. If it is not sunny and it is snowing then Pedro goes hunting.

  2. If it is windy and Pedro does not go hunting then it is not snowing.

  3. If it is windy and not sunny then Pedro goes hunting.

  4. If it is windy and sunny then Pedro goes hunting.

Show answer
Correct Option: B

AI Explanation

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

Option A) If it is not sunny and it is snowing then Pedro goes hunting. This statement is not necessarily true. According to the given conditions, if it is snowing and windy, Pedro goes hunting. However, it does not specify what Pedro does if it is not sunny and snowing. Pedro could either go hunting or fishing in this case, so this statement is not necessarily true.

Option B) If it is windy and Pedro does not go hunting then it is not snowing. This statement is correct. According to the given conditions, if it is snowing and windy, Pedro goes hunting. Therefore, if Pedro does not go hunting, it means it is not snowing. So, this statement must be true.

Option C) If it is windy and not sunny then Pedro goes hunting. This statement is not necessarily true. According to the given conditions, if it is sunny and not windy, Pedro goes fishing. However, it does not specify what Pedro does if it is windy and not sunny. Pedro could either go hunting or fishing in this case, so this statement is not necessarily true.

Option D) If it is windy and sunny then Pedro goes hunting. This statement is not necessarily true. According to the given conditions, if it is sunny and not windy, Pedro goes fishing. It does not specify what Pedro does if it is windy and sunny. Pedro could either go hunting or fishing in this case, so this statement is not necessarily true.

The correct answer is B. If it is windy and Pedro does not go hunting, then it is not snowing. This statement is correct because if it is snowing and windy, Pedro goes hunting. Therefore, if Pedro does not go hunting, it means it is not snowing.

The cost of manufacturing tractors in Korea is twenty percent less than the cost of manufacturing tractors in Germany. Even after transportation fees and import taxes are added, it is still cheaper to import tractors from Korea to Germany than to produce tractors in Germany. Which of the following assertions is best supported by this information?
general knowledge math & puzzles

  1. Labor costs in Korea are twenty  percent below those in Germany.

  2. Importing tractors into Germany will eliminate twenty  percent of the manufacturing jobs in Germany.

  3. The costs of transporting a tractor  from Korea to Germany is more than twenty  percent of the cost of manufacturing the tractor in Korea.

  4. The import taxes on a tractor  imported from Korea to Germany is less than twenty  percent of the cost of manufacturing the tractor in Germany.

Show answer
Correct Option: D
Explanation:

To solve this question, the user needs to understand the information provided and make logical inferences based on that information.

The passage states that the cost of manufacturing tractors in Korea is twenty percent less than the cost of manufacturing tractors in Germany. Even after transportation fees and import taxes are added, it is still cheaper to import tractors from Korea to Germany than to produce tractors in Germany.

Now let's go through each option and explain why it is right or wrong:

A. Labor costs in Korea are twenty percent below those in Germany. There is no information given about the specific percentage difference in labor costs between Korea and Germany. The passage only states that the cost of manufacturing tractors in Korea is twenty percent less than in Germany. This does not necessarily mean that labor costs are twenty percent below those in Germany. Therefore, this option is not supported by the information given.

B. Importing tractors into Germany will eliminate twenty percent of the manufacturing jobs in Germany. There is no information given about the potential impact on manufacturing jobs in Germany. The passage only states that it is cheaper to import tractors from Korea to Germany, but it does not provide any information about the impact on jobs. Therefore, this option is not supported by the information given.

C. The costs of transporting a tractor from Korea to Germany is more than twenty percent of the cost of manufacturing the tractor in Korea. This option is not supported by the information given. The passage mentions that even after transportation fees and import taxes are added, it is still cheaper to import tractors from Korea to Germany. This suggests that the costs of transporting the tractors are not more than twenty percent of the cost of manufacturing them in Korea. Therefore, this option is not supported by the information given.

D. The import taxes on a tractor imported from Korea to Germany is less than twenty percent of the cost of manufacturing the tractor in Germany. This option is supported by the information given. The passage states that even after transportation fees and import taxes are added, it is still cheaper to import tractors from Korea to Germany. This implies that the import taxes on the tractors are less than twenty percent of the cost of manufacturing them in Germany. Therefore, this option is supported by the information given.

The Answer is: D

In 1695 about 11,400 doctors who had treated plague sufferers died and about 23,670 doctors who had not treated plague sufferers died. On the basis of these figures, it can be concluded that it was more dangerous for doctors not to participate in the treatment of plague sufferers than it was for them to participate in it. Which of the following statements would cast most doubt on the conclusion above?
general knowledge math & puzzles

  1. Examining the death rates for doctors in the years before and after 1695.

  2. Separating deaths due to natural causes during the treatment of plague suffers from deaths caused by other causes.

  3. Comparing death rates per thousand members of each group rather than comparing total numbers of deaths.

  4. The figures quoted may vary by plus or minus ten percent from the actual figures.

Show answer
Correct Option: C
Explanation:

To solve the question, let's analyze each statement and determine which one casts the most doubt on the conclusion:

A. Examining the death rates for doctors in the years before and after 1695.

This statement would provide additional information about the death rates of doctors in different time periods, which could help determine if the death rates during 1695 were significantly different or not. If the death rates were similar in other years, it would suggest that the deaths in 1695 may not be directly related to treating plague sufferers. Therefore, this statement could cast doubt on the conclusion.

B. Separating deaths due to natural causes during the treatment of plague sufferers from deaths caused by other causes.

This statement suggests that deaths during the treatment of plague sufferers could be caused by factors unrelated to the treatment itself. By isolating deaths caused by other factors, it would help determine if treating plague sufferers directly contributed to the higher death rates among doctors. This statement provides valuable information but doesn't directly cast doubt on the conclusion.

C. Comparing death rates per thousand members of each group rather than comparing total numbers of deaths.

This statement suggests comparing death rates per thousand members of each group, which would give a more accurate representation of the risk involved. It could reveal that the death rates among doctors who treated plague sufferers were relatively higher compared to their overall population, indicating a higher risk. Conversely, it could also show that the death rates among doctors who didn't treat plague sufferers were relatively higher compared to their population, casting doubt on the conclusion. Therefore, this statement could potentially cast doubt on the conclusion.

D. The figures quoted may vary by plus or minus ten percent from the actual figures.

This statement implies a margin of error in the figures provided. While it's important to consider the accuracy of the data, it doesn't directly challenge the conclusion based on the given figures. It might affect the precision of the conclusion, but it doesn't provide contradictory information.

Therefore, based on the analysis above, the statement that would cast the most doubt on the conclusion is:

C. Comparing death rates per thousand members of each group rather than comparing total numbers of deaths.

My sister 6 years younger than me and my brother is 12 years younger than me . IF my bother's age is 11 than how old is my sister?

general knowledge math & puzzles

  1. 18

  2. 17

  3. 20

  4. 24

Show answer
Correct Option: B

Of the teams competing in the world archery championships, twenty percent are from Europe. Half as many are from the United States and one twentieth are from Africa. What fraction of teams are from neither Europe, the US or Africa.
general knowledge math & puzzles

  1. 13/20

  2. 15/20

  3. 13/15

  4. 17/20

Show answer
Correct Option: A
Explanation:

To solve this question, the user needs to know basic arithmetic and the concept of fractions. We can start by adding the fractions that represent the proportion of teams from Europe, the US, and Africa:

20% = 1/5 (Europe)

1/2 (US)

1/20 (Africa)

To find the fraction of teams from neither Europe, the US or Africa, we need to subtract the sum of these fractions from 1 (which represents the total proportion of teams):

1 - (1/5 + 1/2 + 1/20) = 1 - (8/20) = 12/20

Simplifying 12/20 to lowest terms, we get:

12/20 = 3/5

Therefore, the fraction of teams from neither Europe, the US or Africa is 3/5.

Option B (15/20) is incorrect because it is the same as 3/4, which is not equal to 3/5.

Option C (13/15) is incorrect because it is greater than 1 (the total proportion of teams).

Option D (17/20) is incorrect because it is greater than 1 (the total proportion of teams).

The Answer is: A (13/20).

There are 900 bottles to be filled. Jim and Molly working independently but at the same time take 30 minutes to fill the bottles. How long should it take Molly working by herself to fill the bottles?

Statement 1 - Molly fills half as many bottles as Jim.

Statement 2 - Jim would take 45 minutes by himself.

Which of the statements above make it possible to answer the question.
general knowledge math & puzzles

  1. Statement 1 alone is sufficient, but statement 2 alone is not sufficient.

  2. Statement 2 alone is sufficient, but statement 1 alone is not sufficient.

  3. Both statements together are sufficient, but neither statement alone is sufficient.

  4. Each statement alone is sufficient

Show answer
Correct Option: D
Explanation:

To solve this question, you need to know how to set up a system of equations using the given information and how to solve for the unknown variable. Here is one possible explanation:

Let $x$ be the number of bottles that Jim fills in one minute and $y$ be the number of bottles that Molly fills in one minute. Then, we have the following equations:

  • $x + y = 30$ (the total number of bottles filled by Jim and Molly in one minute $\frac{900}{30}$)

Statement 1 tells us that $y = x/2$, which means that Molly fills half as many bottles as Jim in one minute. We can substitute this into the first equation and get:

  • $x + x/2 = 30$
  • $3x/2 = 30$
  • $x = 20$

This means that Jim fills 20 bottles in one minute and Molly fills 10 bottles in one minute. We can use this to find how long it takes Molly to fill the bottles by herself:

  • $30y = 900$
  • $30(10) = 900$
  • $y = 30$

So, Molly takes 30 minutes by herself to fill the bottles. Therefore, statement 1 alone is sufficient to answer the question.

Statement 2 tells us that $45x = 900$, which means that Jim would take 45 minutes by himself to fill the bottles. We can solve for x and get:

  • $x = 20$

This is the same as what we found from statement 1, so we can use it to find how long it takes Molly to fill the bottles by herself:

  • $y = x/2$
  • $y = 20/2$
  • $y = 10$

So, Molly fills 10 bottles in one minute and takes 30 minutes by herself to fill the bottles. Therefore, statement 2 alone is also sufficient to answer the question.

Since both statements alone are sufficient, the correct answer is D. Each statement alone is sufficient.

Mr. Brown has 6 black gloves and 8 brown gloves in his closet. He blindly picks up some gloves from the closet. What is the minimum number of gloves Mr. Brown will have to pick to be certain to find a pair of gloves of the same color?
general knowledge math & puzzles

  1. 2

  2. 3

  3. 7

  4. 9

Show answer
Correct Option: B

Suppose 6 monkeys take 6 minutes to eat 6 bananas. How many monkeys would it take to eat 54 bananas in 54 minutes?
general knowledge math & puzzles

  1. 54

  2. 27

  3. 6

  4. 12

Show answer
Correct Option: C

A painting job can be completed by 3 painters in 29 days. If 6 more painters join the team 2 days after starting work on the job, then how many more days are required to complete the job?

general knowledge math & puzzles

  1. 7

  2. 8

  3. 9

  4. 10

Show answer
Correct Option: C

AI Explanation

To solve this problem, we can use the concept of work rates.

Let's assume that the rate at which one painter can complete the job is 1 unit per day. Therefore, the combined work rate of 3 painters is 3 units per day.

We are given that the job takes 29 days to complete with 3 painters. Therefore, the total work required to complete the job is 3 units/day * 29 days = 87 units.

Now, let's consider the scenario where 6 more painters join the team after 2 days. This means that for the first 2 days, only the initial 3 painters were working.

In these 2 days, the work completed by the initial 3 painters is 3 units/day * 2 days = 6 units. Therefore, the remaining work to be completed is 87 units - 6 units = 81 units.

Now, the combined work rate of 9 painters is 9 units/day.

To find the number of days required to complete the remaining work, we can divide the remaining work by the combined work rate of 9 painters:

Remaining work / Combined work rate = 81 units / 9 units/day = 9 days.

Therefore, the additional number of days required to complete the job is 9.

The correct answer is C) 9.