To answer this question, we can use the concept of similar triangles.

Let's consider the first situation where the pillar is 8 feet tall and casts a shadow that is 4 feet long.

We can set up a proportion between the height of the pillar and the length of its shadow:

$\frac{8}{4} = \frac{16}{x}$

Simplifying this proportion, we have:

$\frac{2}{1} = \frac{16}{x}$

Cross-multiplying, we get:

$2x = 16$

Dividing both sides by 2, we find:

$x = 8$

Therefore, when the pillar is 16 feet tall, the length of its shadow would be 8 feet.

So, the correct answer is A) 8.

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To solve this problem, let's first calculate the rate at which the painters work.

We are given that 5 painters can complete the job in 8 days. This means that the total work done by the painters is 1 job.

Let "R" represent the rate of work done by each painter. Therefore, the rate at which 5 painters work together is 5R.

We can set up the following equation to represent the work done in 8 days:

[5R \times 8 = 1]

Simplifying this equation, we have:

[40R = 1]

Now, let's consider the scenario when 5 more painters join the team after 4 days.

The initial 5 painters worked for 4 days, so the amount of work done by them is (5R \times 4 = 20R).

The remaining work to be done is (1 - 20R).

Now, the total number of painters is 5 + 5 = 10 painters.

We can set up the following equation to represent the work done by the 10 painters:

[10R \times D = 1 - 20R]

where "D" represents the number of additional days required to complete the job.

Simplifying this equation, we have:

[10RD = 1 - 20R]

Since we want to find the number of additional days required to complete the job, we need to find the value of "D".

To solve for "D", let's substitute the value of (R) from the first equation into the second equation:

[10 \times \frac{1}{40} \times D = 1 - 20 \times \frac{1}{40}]

Simplifying this equation, we have:

[\frac{D}{4} = 1 - \frac{1}{2}]

[\frac{D}{4} = \frac{1}{2}]

Multiplying both sides of the equation by 4, we get:

[D = 2]

Therefore, it will take an additional 2 days to complete the job.

The correct answer is option D) 2.

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To answer this question, you need to understand the concept of the Pigeonhole Principle. The Pigeonhole Principle states that if you have more items than the number of containers, then at least one container must contain more than one item.

In this case, we have 12 black socks and 12 white socks, which totals 24 socks. To guarantee that we have a matching pair, we need to take out socks until we have more than 12 socks, as there are only 12 different colors (black and white).

Let's go through each option to determine the smallest number of socks you need to take out to be sure of having a matching pair:

Option A) 5 - If you take out 5 socks blindly, it is possible that you could have taken 3 black socks and 2 white socks, or vice versa. In this case, you do not have a matching pair yet.

Option B) 7 - If you take out 7 socks blindly, it is possible that you could have taken 4 black socks and 3 white socks, or vice versa. In this case, you do not have a matching pair yet.

Option C) 3 - If you take out 3 socks blindly, it is possible that you could have taken 2 black socks and 1 white sock, or vice versa. In this case, you still do not have a matching pair yet.

Option D) 1 - If you take out 1 sock blindly, regardless of the color, you cannot guarantee a matching pair. Therefore, this option is incorrect.

The correct answer is Option C) 3. This option is correct because by taking out 3 socks blindly, you can guarantee that you have a matching pair.

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