4) 196

Explanation: we have all squares of numbers between 6 and 13 so I guess it must be 14^2 = 196

13

The numbers are 3, 11, 13, 23, 31, 41, 43, 53, 61, 71, 73, 83, 91

Only the numbers that end in 1, 3 will have odd remainder so we need to only check the prime numbers which end in 1 and 3

301, 721, etc.

My explanation:

the number is a multiple of LCM of (2,3,4,5,6) + 1 = 60*x + 1

And this number should be divisible by 7.

It’s easy to see the above number will always end up with the number 1. There’s only one multiple of 7 which ends in 1, i.e., 3 (7*3 = 21).

So we only need to check all prime numbers that end in 3. For example, 7 * 13, 7 * 23, 7 * 43, etc. because only these multiples of 7 will result in a number that ends in 1 and also the multiple has to be prime or else it’ll be divisible by either 2, 3 or 5 negating the above condition of leaving one egg.

so we can check all such numbers multiplied by 7 and subtract 1 and check if the number is also a multiple of 60::

7 * 13 = 91 – 1 = 90 (not a multiple of 60)
7 * 23 = 161 – 1 = 160 (not a multiple of 60)
(33 is not a prime number so we don’t need to check that)
7 * 43 = 301 – 1 = 300 (multiple of 6) (Answer)
and we can find many more numbers like this
7 * 53
7 * 73
7 * 83
7 * 103 = 721

b. Just before serving

i = 5, j = 8

This statement,: j = i+++ ++, i is actually

j = i++ + ++i;

i = 3 at first, then starting from left we look at i++, so the expression takes the values as 3 because i++ is a post-increment and afterwards increments i to 4. Then it looks at the other part of the expression which is ++i so for this it does a pre-increment and i becomes 5 and then 3 + 5 is added together and assigned to j.

Assuming the ship is sinking and hence water is rising around it.

Since the bottom rung touches the water already and we need to only find when the water would reach top rung, i.e. water needs to travel 270 cm – 30 – 30 = 210 cm

210 cm / 15 cm/hr = 14 hours

So it’ll take 14 hours for water to reach top rung.

We can understand this more easily by breaking down the solution. Let’s say there were 2 ants and both started at the end, and meet in the middle, and then turn in opposite directions and then fall off the stick. So both have completed 1/2 + 1/2 = 1 stick and so takes 1 minute.

Similarly we can work out this with 3 ants and putting them randomly and check out what happens in each scenario. In all cases time <= 1 minute.So 1 minute (time taken for 1 ant to cross the stick) is the answer.

My answer is also 1/2. By the time my turn comes, 99 seats are already occupied and only 1 is left. So the probability of having that 1 seat assigned or not is 1/2.