Explanation : 

In a tournament of Chess

In a knockout chess tournament like this, each player is eliminated after losing a match. Since there are 150 entrants, only one player remains undefeated at the end of the tournament, and this player is the winner.

To find out how many matches are played, we can think about it in terms of elimination: for every player except the winner, they have to lose exactly one match to be eliminated. Since there are 150 entrants and only one winner, 150 – 1 = 149 players need to be eliminated.

Each elimination comes from one match, so there are 149 matches played in the entire tournament.

Explanation : 

X and Y run a 3 km race

The faster runner will cross the slower one when he covers an extra 300 m. Let their speeds be 3 m/sec and 2 m/sec. So, their relative speed = 3 – 2 = 1 m/sec. So, the time taken by the faster runner to cross the slower one = Distance/Relative Speed = 300/1 = 300 seconds.

It basically means that the faster runner will cross the slower one every 300 seconds or 5 minutes. Now, the time taken for the faster racer to complete the entire race = Total Distance/Speed = 3000/3 =1000 seconds.

So, during the entire race, which lasts for 1000 seconds, the faster racer will cross the slower one 3 times – after 300 seconds, 600 seconds, and 900 seconds.

Explanation : 

A has some coins

Let’s say A had x coins in the beginning.
After giving half of the coins and 2 more to B, A has (x/2) – 2 coins left and B has (x/2) + 2 coins.
After B gives half of the coins and 2 more to C, B has ((x/2) + 2)/2 – 2 = (x/4) – 1 coins left and C has ((x/2) + 2)/2 + 2 = (x/4) + 3 coins.
After C gives half of the coins and 2 more to D, C has ((x/4) +3)/2 – 2 = (x/8) -1/2 coins left and D has ((x/4)+3)/2+2 = (x/8)+7/2 coins.

Since D has the smallest two-digit number which is 10, we can set up an equation: (x/8)+7/2 =10. Solving for x we get: x=52.

So A had 52 coins in the beginning.

Explanation : 

A B C are three places

One can travel from A to C in 15 different ways. There are two possible routes: directly from A to C or from A to B and then from B to C.

The number of ways to travel directly from A to C is 3 (since there are 3 different roads). The number of ways to travel from A to B and then from B to C is the product of the number of roads between each pair of places: 3 x 4 = 12.

So, in total, there are 3 + 12 = 15 different ways one can travel from A to C using these roads.

Explanation : 

101 plants on a 1.01 km road

Let’s say we have a road that is 1.01 km long. On one side of the road, there are 101 plants planted at equal distances from each other. We can convert the length of the road to meters: 1.01 km * 1000 m/km = 1010 m.

Now, imagine that the plants are represented by dots on a number line. The first plant is at position 0 and the last plant is at position 1010. Since there are 101 plants in total, there must be 100 gaps between them.

We can find the distance between two consecutive plants by dividing the total distance (1010 m) by the number of gaps (100): 1010 m / 100 = 10.1 m.

So, if we want to find the total distance between five consecutive plants, we need to multiply this distance (10.1 m) by one less than the number of plants because for 5 Consecutive Plants, gaps between them is 4 (5-1=4): 10.1 m * 4 = 40.4 m.

Explanation : 

Letters A B C D and E are arranged

The problem asks for the number of arrangements of the letters A, B, C, D and E such that there are exactly two letters between A and E. There are four possible arrangements for A and E: A _ _ E _, _ A _ _ E, E _ _ A _, and _ E _ _ A. For each of these arrangements, there are 3! = 6 ways to arrange the remaining letters B, C and D. So the total number of arrangements is 4 * 6 = 24.

Explanation : 

Total number of seconds in x weeks, x days, x hours, x minutes and x seconds is 694861x.

So the correct answer is d. 694861x.

Here’s how you can calculate it: 1 week = 7 days 1 day = 24 hours 1 hour = 60 minutes 1 minute = 60 seconds

So, x weeks = (7 * 24 * 60 * 60) * x seconds x days = (24 * 60 * 60) * x seconds x hours = (60 * 60) * x seconds x minutes = (60) * x seconds

Adding all of these together with the additional x seconds gives us: 604800x + 86400x + 3600x + 60x + x=694861x