Solution:

Route(Root symbol) + 66
= Route66

Solution:

1:1 (approx)

Explanation:
We know that the probability of having a boy or having a girl is same and thus, half of the couples will stop after having a boy child. Half of the others will have a girl and will have a baby again. Out of those half of the couples, half will have a boy and will stop and half will have a girl again. This will keep on going like this.

Now, if there are X number of couples, there will be X boys.

1/2 have a boy and stop: 0 girls
1/4 have a girl, then a boy: X/4 girls
1/8 have 2 girls, then a boy: 2*X/8 girls
1/16 have 3 girls, then a boy: 3*X/16 girls
1/32 have 4 girls, then a boy: 4*X/32 girls
…
Total: X boys and
1X 2X 3X 4X
– + – + – + — +… = ~X

Therefore, the proportion of boys to girls will be extremely close to 1:1

Solution:

A typical way will be to start thinking about summing up the distance that the bee will travel but that will be quite a tedious task. How about we offer you a much easy solution?

The tunnel is 200 miles long and the trains are running at as peed of 100 mph which means that they will collide exactly at the center of the tunnel and seeking their speed, they will collide after an hour.

Now consider the bee which is flying at a speed of 1000 mph and will keep flying till the train collides. As calculated, it will keep flying for an hour which means the distance that it will cover is 1000 miles.

Solution:

(0! + 0! + 0!)! = 6
(1 + 1 + 1)! = 6
2 + 2 + 2 = 6
3 x 3 - 3 = 6
√4 + √4 + √4 = 6
5 + 5/5 = 6
6 + 6 - 6 = 6
7 - 7/7 = 6
8 - √√(8 + 8) = 6
√(9 x 9) - √9 = 6

Solution:

5050

Explanation:
You must have noticed that 50 pairs of n^2 – (n-1) ^2 exist.
n^2 – (n-1)^2 = n + (n – 1)

In such case, we may as well write 100^2 - 99^2 + 98^2 - 97^2 + 96^2 - 95^2 + ... + 2^2 - 1^2 as 100 + 99 + 98+ ... + 2 + 1 = (100 x 101)/2 = 5050

Solution:

What must be kept in mind before you start calculating through any method is that the weights can be put on both the pans.

So the weights - 1, 3, 7, 12, 43, 76, 102

The oldest man that can be weighed using these weights is a man aged 122 years

Solution:

This problem can be solved with similar triangles property.
The White triangle is similar to the Red one
Now Ratio of sides is 2:3 (as ratio of areas = ratio of based if the height is same)
Seeking that, White triangle = 9/4 * Yellow triangle = 9/2
Following all the above, the Green region = 5.5 units

Solution:

12

Explanation:
The amount won and lost by both is equal.
Thus 2x = 3(20-x) --- x in the number of times heads came
X = 12

Solution:

25%

Suppose every item is priced at $100. On 20% discount, the price will become $80. Now he must add $20 to each item for original price which is 25% of $80.

Solution:

t1 + t2 = 100 minutes = 100/60 hours
t1 = x/55
t2 = (x+20)/40

x/55 + (x+20)/40 = 100/60
x = 1540/57

Total distance = x + (x+20) = 4220/57 miles = 74 2/57 miles