Solution:

If you remember the formulas, you will find out that the first option cannot exist.
Side A^2 + Side B^2 = Side C^2

Thus the only possible option here is the second one and of course, it will have a greater area then

Solution:

Since every bacterium divides into two in two minutes and we know the fact that the dish was half filled with bacteria at 3 pm, after exactly 2 minutes, all will divide into two and will fill the petri dish. Thus, the petri dish will become full at 3:02 pm.

Solution:

4

Explanation:
Now if you go on calculating 2^300, you will lose so much time and it might not even be feasible to carry out so long of calculations. Thus we will make use of a trick here. We will calculate the remainder of each power of 2 till we come across a pattern.

2^1 divided by 4 leaves the remainder 2.
2^2 divided by 4 leaves the remainder 0.
2^3 divided by 4 leaves the remainder 0.
2^4 divided by 4 leaves the remainder 0.

You can see that all the following powers of two will be divisible by 4. Therefore the remainder when 2^300 is divided by 4 will be 0 only.

Solution:

16/81

Explanation:
It is a question of geometric progression but we can solve it step by step as well in case you are not aware of the formula.

At first bounce
The height at which the ball would have reached = 2/3 of the original height from which it was dropped.

At second bounce
The height at which the ball would have reached = 2/3 * 2/3 of the original height from which it was dropped.

At third bounce
The height at which the ball would have reached = 2/3 * 2/3 * 2/3 of the original height from which it was dropped.

At fourth bounce
The height at which the ball would have reached = 2/3 * 2/3 * 2/3 * 2/3 of the original height from which it was dropped.

Now, 2/3 * 2/3 * 2/3 * 2/3 = 16/81

Therefore, 16/81 of the original height from which the ball was dropped is the required fraction height.

Solution:

The chances that the pair you take out is a white pair is zero.

Just analyze the statement carefully. If there are two colored socks in a drawer, there can be three chances if you take out a pair. It can be either black socks or white socks or a mixed of two. But as per the statement the chances of taking out a black pair of socks is 1/2. Therefore, only two chances exist. We do know that there is a mix of white and black socks in the drawer and thus the second chance has to be a mixture of them both. This is the reason why we can deduce that there are three black socks in the drawer and just one white sock. Thus the probability of taking out two white socks will be zero.

Solution:

10 percent of student study all four subjects.

Solution:

Of course, the questions has so many details and so many figures, but you have to consider just a few things. First calculate how much time will it take the friends to meet. Since they are meeting half way, they have to travel 18 miles. At the speed of 6 MPH, they will be able to do it in three hours.

Now see the fact that the parrot will keep on flying for three hours at 20 MPH. Thus the total distance that will be covered will be 60 miles.

Solution:

Augustus and Joshua play all the three sports. Stacy plays none.

This is when we have assumed that girls do not play football at all. If by any means, the school has a girl's football league, all we know is that one of the three play no sports at all and the others play all the three.

Solution:

b+g = 8

Explanation:
for b in range(1,99):
for g in range(1,99):
sum1=2*b*g+42
sum2=(b+g)*(b+g+1)
if(sum1==sum2):
print(b,g,sum1)

(b,g)=(3,5) => b+g=8

Solution:

The easiest method to solve this question will be to form equations.

From the first picture
Weight of Cat + Weight of Rabbit = 10 Kg ---- First Equation

From the second picture
Weight of Dog + Weight of Rabbit = 20 Kg ---- Second Equation

From third picture
Weight of Cat + Weight of Dog = 24 Kg ---- Third Equation

Add the first, second and the third equations.

2 (Weight of Cat) + 2 (Weight of Dog) + 2 (Weight of Rabbit) = 10 Kg + 20 Kg + 24 Kg
2 (Weight of Cat + Weight of Dog + Weight of Rabbit) = 54 Kg
Weight of Cat + Weight of Dog + Weight of Rabbit = 27 Kg