To solve this question, we can use the concept of ratios and proportions.

Let's analyze the given information:

• 8 crows can steal 8 buttons in 8 minutes.

From this, we can infer that each crow can steal 1 button in 8 minutes.

Now, let's use this information to find out how many buttons can 16 crows steal in 16 minutes.

Since each crow can steal 1 button in 8 minutes, in 16 minutes, each crow can steal 2 buttons (as the time has doubled).

Therefore, 16 crows can steal 2 buttons each in 16 minutes.

So, the total number of buttons that 16 crows can steal in 16 minutes is:

16 crows * 2 buttons/crow = 32 buttons

Therefore, the correct answer is option B) 32.

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To solve this problem, let's assume the current age of the ship as 'S' and the current age of the ship's boiler as 'B'.

According to the given information, the ship is currently twice as old as the ship's boiler was when the ship was as old as the boiler is.

So, when the ship was as old as the boiler is, the age of the ship was 'B' and the age of the boiler was 'B'.

Therefore, we can write the equation:

S = 2(B - S)

Solving this equation will give us the ratio of the boiler's age to the ship's age.

Expanding the equation, we get:

S = 2B - 2S

Adding '2S' to both sides:

S + 2S = 2B

Combining like terms:

3S = 2B

Dividing both sides by 'B':

(3S) / (2B) = 1

Simplifying the expression, we get:

(3/2)(S/B) = 1

Therefore, the ratio of the boiler's age to the ship's age is 3/2, which is equivalent to 3/4.

Hence, the correct answer is D) 3/4.

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To find the number of handshakes, we can use the combination formula.

In this case, there are 12 members at the meeting, and each member shakes hands with all the other members.

To calculate the number of handshakes, we need to find the number of combinations of 2 members chosen from a group of 12.

The formula for combinations is given by: $$\binom{n}{r} = \frac{n!}{r!(n-r)!}$$

In this case, we have: $$\binom{12}{2} = \frac{12!}{2!(12-2)!} = \frac{12!}{2!10!}$$

Calculating the factorials: $$12! = 12 \times 11 \times 10!$$ $$2! = 2 \times 1$$ $$10! = 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1$$

Plugging in the values: $$\binom{12}{2} = \frac{12 \times 11 \times 10!}{2 \times 1 \times 10!}$$

Simplifying: $$\binom{12}{2} = \frac{12 \times 11}{2}$$

$$\binom{12}{2} = 66$$

Therefore, the correct answer is option C) 66.

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To solve this question, we need to think beyond letter series. Let's analyze the given series:

C D I L M V ?

If we observe the given series closely, we can see that it follows the pattern of Roman numerals. The series starts with "C" which represents the Roman numeral for 100, followed by "D" which represents 500. Then, we have "I" which represents 1, "L" represents 50, "M" represents 1000, and finally, "V" represents 5.

The pattern in the series is that each subsequent element represents a decreasing value in Roman numerals. Therefore, the next element in the series should represent the Roman numeral for a value less than 5.

Let's go through each option to determine the correct answer:

Option A) Z - This option is incorrect because "Z" does not represent a Roman numeral value less than 5. Option B) X - This option is correct because "X" represents the Roman numeral for 10, which is less than 5. Option C) W - This option is incorrect because "W" does not represent a Roman numeral value less than 5. Option D) A - This option is incorrect because "A" does not represent a Roman numeral value.

Therefore, the correct answer is option B) X.

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To solve this question, we need to look for a pattern or sequence in the given series: M V E M J S U N ?.

If we observe closely, we can see that each letter in the series represents the first letter of the names of the planets in our solar system in reverse order.

M - Mercury V - Venus E - Earth M - Mars J - Jupiter S - Saturn U - Uranus N - Neptune

So, the missing letter in the series is the first letter of the planet before Neptune, which is P.

Therefore, the correct answer is D) P.

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To solve the given expression, we can use the trigonometric identity:

[ \tan(A) \cdot \tan(B) = \frac{{\sin(A) \cdot \sin(B)}}{{\cos(A) \cdot \cos(B)}} ]

Let's evaluate each option to determine if it is correct or not:

Option A) 0 - This option is incorrect because the product of the tangents of two angles is not necessarily zero.

Option B) 1 - This option is correct. By substituting the values of the angles, we have:

[ \tan(30) \cdot \tan(60) = \frac{{\sin(30) \cdot \sin(60)}}{{\cos(30) \cdot \cos(60)}} = \frac{{\frac{1}{2} \cdot \frac{\sqrt{3}}{2}}}{{\frac{\sqrt{3}}{2} \cdot \frac{1}{2}}} = 1 ]

Option C) sin 90 - This option is correct. By substituting the values of the angles, we have:

[ \tan(30) \cdot \tan(60) = \frac{{\sin(30) \cdot \sin(60)}}{{\cos(30) \cdot \cos(60)}} = \frac{{\frac{1}{2} \cdot \frac{\sqrt{3}}{2}}}{{\frac{\sqrt{3}}{2} \cdot \frac{1}{2}}} = 1 ]

Since (\sin(90) = 1), this option is correct.

Option D) cos 0 - This option is correct. By substituting the values of the angles, we have:

[ \tan(30) \cdot \tan(60) = \frac{{\sin(30) \cdot \sin(60)}}{{\cos(30) \cdot \cos(60)}} = \frac{{\frac{1}{2} \cdot \frac{\sqrt{3}}{2}}}{{\frac{\sqrt{3}}{2} \cdot \frac{1}{2}}} = 1 ]

Since (\cos(0) = 1), this option is correct.

Option E) tan 45 - This option is correct. By substituting the values of the angles, we have:

[ \tan(30) \cdot \tan(60) = \frac{{\sin(30) \cdot \sin(60)}}{{\cos(30) \cdot \cos(60)}} = \frac{{\frac{1}{2} \cdot \frac{\sqrt{3}}{2}}}{{\frac{\sqrt{3}}{2} \cdot \frac{1}{2}}} = 1 ]

Since (\tan(45) = 1), this option is correct.

Therefore, the correct options are B, C, D, and E.

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To find the total number of toes in the bus, we need to calculate the number of toes for each component and then add them together.

Given:

• 4 children in the bus, and each child has 4 backpacks with them.
• There are 4 dogs sitting in each backpack, and each dog has 4 puppies.
• Each dog has 4 legs, with 4 toes on each leg.

Let's break down the calculation:

1. Number of toes for the children: Each child has 2 legs, and each leg has 5 toes (including the big toe). So, each child contributes 2 x 5 = 10 toes. Since there are 4 children, the total number of toes for the children is 4 x 10 = 40 toes.

2. Number of toes for the dogs: Each dog has 4 legs, and each leg has 4 toes. So, each dog contributes 4 x 4 = 16 toes. Since there are 4 dogs in each backpack, and each child has 4 backpacks, the total number of toes for the dogs is 4 x 4 x 4 = 64 toes.

3. Number of toes for the puppies: Each puppy has 4 legs, and each leg has 4 toes. So, each puppy contributes 4 x 4 = 16 toes. Since there are 4 puppies with each dog, the total number of toes for the puppies is 4 x 16 = 64 toes.

Now, let's calculate the total number of toes in the bus:

Total number of toes = (toes for children) + (toes for dogs) + (toes for puppies) = 40 + 64 + 64 = 168

Therefore, the total number of toes in the bus is 168.

However, none of the given options match the calculated result. Please check the question and options again.

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